BuyFind*launch*

10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 5.2, Problem 3E

Textbook Problem

**Finding u and du/dx** In Exercises 1-8, identify

Calculus: An Applied Approach (MindTap Course List)

Ch. 5.1 - Checkpoint 1 Worked-out solution available at...Ch. 5.1 - Checkpoint 2 Worked-out solution available at...Ch. 5.1 - Checkpoint 3 Worked-out solution available at...Ch. 5.1 - Checkpoint 4 Worked-out solution available at...Ch. 5.1 - Checkpoint 5 Worked-out solution available at...Ch. 5.1 - Checkpoint 6 Worked-out solution available at...Ch. 5.1 - Checkpoint 7 Worked-out solution available at...Ch. 5.1 - Checkpoint 8 Worked-out solution available at...Ch. 5.1 - In Exercises 1-6, rewrite the expression using...Ch. 5.1 - In Exercises 1-6, rewrite the expression using...

Ch. 5.1 - In Exercises 1-6, rewrite the expression using...Ch. 5.1 - In Exercises 1-6, rewrite the expression using...Ch. 5.1 - In Exercises 1-6, rewrite the expression using...Ch. 5.1 - In Exercises 1-6, rewrite the expression using...Ch. 5.1 - In Exercises 7-10, let (x, y) = (2, 2), and solve...Ch. 5.1 - In Exercises 7-10, let (x, y) = (2, 2), and solve...Ch. 5.1 - In Exercises 7-10, let (x, y) = (2, 2), and solve...Ch. 5.1 - In Exercises 7-10, let (x, y) = (2, 2), and solve...Ch. 5.1 - Integration and Differentiation In Exercises 1- 6,...Ch. 5.1 - Integration and Differentiation In Exercises 1- 6,...Ch. 5.1 - Integration and Differentiation In Exercises 1- 6,...Ch. 5.1 - Integration and Differentiation In Exercises 1- 6,...Ch. 5.1 - Integration and Differentiation In Exercises 1- 6,...Ch. 5.1 - Integration and Differentiation In Exercises 1-6,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 7-18,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 7-18,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 7-18,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 7-18,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 7-18,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 7-18,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 7-18,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 7-18,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 7-18,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 7-18,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 7-18,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 7-18,...Ch. 5.1 - Rewriting Before Integrating In Exercises 19-24,...Ch. 5.1 - Rewriting Before Integrating In Exercises 19-24,...Ch. 5.1 - Rewriting Before Integrating In Exercises 19-24,...Ch. 5.1 - Rewriting Before Integrating In Exercises 19-24,...Ch. 5.1 - Rewriting Before Integrating In Exercises 19-24,...Ch. 5.1 - Rewriting Before Integrating In Exercises 19-24,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 25-36,...Ch. 5.1 - Finding Indefinite Integrals In Exercises 25-36,...Ch. 5.1 - Finding indefinite integrals In Exercises 2536,...Ch. 5.1 - Finding indefinite integrals In Exercises 2536,...Ch. 5.1 - Finding indefinite integrals In Exercises 2536,...Ch. 5.1 - Finding indefinite integrals In Exercises 2536,...Ch. 5.1 - Finding indefinite integrals In Exercises 2536,...Ch. 5.1 - Finding indefinite integrals In Exercises 2536,...Ch. 5.1 - Finding indefinite integrals In Exercises 2536,...Ch. 5.1 - Finding indefinite integrals In Exercises 2536,...Ch. 5.1 - Finding indefinite integrals In Exercises 2536,...Ch. 5.1 - Finding indefinite integrals In Exercises 2536,...Ch. 5.1 - Using Technology In Exercises 37 and 38, use a...Ch. 5.1 - Using Technology In Exercises 37 and 38, use a...Ch. 5.1 - Interpreting a Graph In Exercises 3942, the graph...Ch. 5.1 - Interpreting a Graph In Exercises 3942, the graph...Ch. 5.1 - Interpreting a Graph In Exercises 3942, the graph...Ch. 5.1 - Interpreting a Graph In Exercises 3942, the graph...Ch. 5.1 - Finding a Particular Solution In Exercises 4350,...Ch. 5.1 - Finding a Particular Solution In Exercises 4350,...Ch. 5.1 - Finding a Particular Solution In Exercises 4350,...Ch. 5.1 - Finding a Particular Solution In Exercises 4350,...Ch. 5.1 - Finding a Particular Solution In Exercises 4350,...Ch. 5.1 - Finding a Particular Solution In Exercises 4350,...Ch. 5.1 - Finding a Particular Solution In Exercises 4350,...Ch. 5.1 - Finding a Particular Solution In Exercises 4350,...Ch. 5.1 - Finding a Particular Solution In Exercises 5154,...Ch. 5.1 - Finding a Particular Solution In Exercises 5154,...Ch. 5.1 - Finding a Particular Solution In Exercises 5154,...Ch. 5.1 - Finding a Particular Solution In Exercises 5154,...Ch. 5.1 - Finding a Cost Function In Exercises 5558, find...Ch. 5.1 - Finding a Cost Function In Exercises 5558, find...Ch. 5.1 - Finding a Cost Function In Exercises 5558, find...Ch. 5.1 - Finding a Cost Function In Exercises 5558, find...Ch. 5.1 - Revenue and Demand In Exercises 59 and 60, find...Ch. 5.1 - Revenue and Demand In Exercises 59 and 60, find...Ch. 5.1 - Profit In Exercises 6164, find the profit function...Ch. 5.1 - Profit In Exercises 6164, find the profit function...Ch. 5.1 - Profit In Exercises 6164, find the profit function...Ch. 5.1 - Profit In Exercises 6164, find the profit function...Ch. 5.1 - Vertical Motion In Exercises 6568, use s(t)=32...Ch. 5.1 - Vertical Motion In Exercises 6568, use s(t)=32...Ch. 5.1 - Vertical Motion In Exercises 6568, use s(t) = 32...Ch. 5.1 - Vertical Motion In Exercises 6568, use s(t) = 32...Ch. 5.1 - Cost A company produces a product for which the...Ch. 5.1 - Gardening An evergreen nursery usually sells a...Ch. 5.1 - Population growth The growth rate of the...Ch. 5.1 - HOW DO YOU SEE IT? The graph shows the rate of...Ch. 5.1 - Vital Statistics The rate of increase of the...Ch. 5.1 - Internet Users The rate of growth of the number of...Ch. 5.1 - Economics: Marginal Benefits and Costs The table...Ch. 5.2 - Checkpoint 1 Worked-out solution available at...Ch. 5.2 - Checkpoint 2 Worked-out solution available at...Ch. 5.2 - Checkpoint 3 Worked-out solution available at...Ch. 5.2 - Checkpoint 4 Worked-out solution available at...Ch. 5.2 - Checkpoint 5 Worked-out solution available at...Ch. 5.2 - Checkpoint 6 Worked-out solution available at...Ch. 5.2 - Checkpoint 7 Worked-out solution available at...Ch. 5.2 - Checkpoint 8 Worked-out solution available at...Ch. 5.2 - In Exercises 1-9, find the indefinite integral....Ch. 5.2 - In Exercises 1-9, find the indefinite integral....Ch. 5.2 - In Exercises 1-9, find the indefinite integral....Ch. 5.2 - In Exercises 1-9, find the indefinite integral....Ch. 5.2 - In Exercises 1-9, find the indefinite integral....Ch. 5.2 - In Exercises 1-9, find the indefinite integral....Ch. 5.2 - In Exercises 1-9, find the indefinite integral....Ch. 5.2 - In Exercises 1-9, find the indefinite integral....Ch. 5.2 - In Exercises 1-9, find the indefinite integral....Ch. 5.2 - Finding u and du/dx In Exercises 1-8, identify u...Ch. 5.2 - Finding u and du/dx In Exercises 1-8, identify u...Ch. 5.2 - Finding u and du/dx In Exercises 1-8, identify u...Ch. 5.2 - Finding u and du/dx In Exercises 1-8, identify u...Ch. 5.2 - Finding u and du/dx In Exercises 1-8, identify u...Ch. 5.2 - Finding u and du/dx In Exercises 1-8, identify u...Ch. 5.2 - Finding u and du/dx In Exercises 1-8, identify u...Ch. 5.2 - Finding u and du/dx In Exercises 1-8, identify u...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 9-34,...Ch. 5.2 - Applying the General Power Rule In Exercises 934,...Ch. 5.2 - Applying the General Power Rule In Exercises 934,...Ch. 5.2 - Applying the General Power Rule In Exercises 934,...Ch. 5.2 - Applying the General Power Rule In Exercises 934,...Ch. 5.2 - Applying the General Power Rule In Exercises 934,...Ch. 5.2 - Applying the General Power Rule In Exercises 934,...Ch. 5.2 - Applying the General Power Rule In Exercises 934,...Ch. 5.2 - Applying the General Power Rule In Exercises 934,...Ch. 5.2 - Applying the General Power Rule In Exercises 934,...Ch. 5.2 - Applying the General Power Rule In Exercises 934,...Ch. 5.2 - Integration by Substitution In Exercises 3542, use...Ch. 5.2 - Integration by Substitution In Exercises 3542, use...Ch. 5.2 - Integration by Substitution In Exercises 3542, use...Ch. 5.2 - Integration by Substitution In Exercises 3542, use...Ch. 5.2 - Integration by Substitution In Exercises 3542, use...Ch. 5.2 - Integration by Substitution In Exercises 3542, use...Ch. 5.2 - Integration by Substitution In Exercises 3542, use...Ch. 5.2 - Integration by Substitution In Exercises 3542, use...Ch. 5.2 - Comparing Methods In Exercises 43-46, (a) perform...Ch. 5.2 - Comparing Methods In Exercises 43-46, (a) perform...Ch. 5.2 - Comparing Methods In Exercises 43-46, (a) perform...Ch. 5.2 - Comparing Methods In Exercises 43-46, (a) perform...Ch. 5.2 - Finding an Equation of a Function In Exercises...Ch. 5.2 - Finding an Equation of a Function In Exercises...Ch. 5.2 - Finding an Equation of a Function In Exercises...Ch. 5.2 - Finding an Equation of a Function In Exercises...Ch. 5.2 - Cost The marginal cost of a product is modeled by...Ch. 5.2 - Cost The marginal cost of a product is modeled by...Ch. 5.2 - Supply In Exercises 53 and 54, find the supply...Ch. 5.2 - Supply In Exercises 53 and 54, find the supply...Ch. 5.2 - Supply In Exercises 53 and 54, find the supply...Ch. 5.2 - Supply In Exercises 53 and 54, find the supply...Ch. 5.2 - Gardening An evergreen nursery usually sells a...Ch. 5.2 - HOW DO YOU SEE IT? The graph shows the rate of...Ch. 5.2 - Marginal Propensity to Consume In Exercises 59 and...Ch. 5.2 - Marginal Propensity to Consume In Exercises 59 and...Ch. 5.2 - Integration Using Technology In Exercises 61 and...Ch. 5.2 - Integration Using Technology In Exercises 61 and...Ch. 5.3 - Checkpoint 1 Worked-out solution available at...Ch. 5.3 - Checkpoint 2 Worked out solution available at...Ch. 5.3 - Checkpoint 3 Worked-out solution available at...Ch. 5.3 - Checkpoint 4 Worked-out solution available at...Ch. 5.3 - Checkpoint 5 Worked-out solution available at...Ch. 5.3 - Checkpoint 6 Worked-out solution available at...Ch. 5.3 - Checkpoint 7 Worked-out solution available at...Ch. 5.3 - In Exercises 14, use long division to rewrite the...Ch. 5.3 - In Exercises 14, use long division to rewrite the...Ch. 5.3 - In Exercises 14, use long division to rewrite the...Ch. 5.3 - In Exercises 14, use long division to rewrite the...Ch. 5.3 - In Exercises 58, find the indefinite integral....Ch. 5.3 - In Exercises 58, find the indefinite integral....Ch. 5.3 - In Exercises 58, find the indefinite integral....Ch. 5.3 - In Exercises 58, find the indefinite integral....Ch. 5.3 - Integrating an Exponential Function In Exercises...Ch. 5.3 - Integrating an Exponential Function In Exercises...Ch. 5.3 - Integrating an Exponential Function In Exercises...Ch. 5.3 - Integrating an Exponential Function In Exercises...Ch. 5.3 - Integrating an Exponential Function In Exercises...Ch. 5.3 - Integrating an Exponential Function In Exercises...Ch. 5.3 - Integrating an Exponential Function In Exercises...Ch. 5.3 - Integrating an Exponential Function In Exercises...Ch. 5.3 - Integrating an Exponential Function In Exercises...Ch. 5.3 - Integrating an Exponential Function In Exercises...Ch. 5.3 - Integrating an Exponential Function In Exercises...Ch. 5.3 - Integrating an Exponential Function In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Using the log Rule for integration In Exercises...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding indefinite integrals In Exercises 3146,...Ch. 5.3 - Finding an Equation of a Function In Exercises...Ch. 5.3 - Finding an Equation of a Function In Exercises...Ch. 5.3 - Finding an Equation of a Function In Exercises...Ch. 5.3 - Finding an Equation of a Function In Exercises...Ch. 5.3 - Biology A population P of bacteria is growing at...Ch. 5.3 - Biology Because of an insufficient oxygen supply,...Ch. 5.3 - Demand The marginal price for the demand of a...Ch. 5.3 - HOW DO YOU SEE IT? The graph shows the rate of...Ch. 5.3 - Revenue The rate of change in revenue for the...Ch. 5.3 - Revenue The rate of change in revenue for DIRECTV...Ch. 5.3 - True or False In Exercises 57 and 58, determine...Ch. 5.3 - True or False In Exercises 57 and 58, determine...Ch. 5.3 - In Exercises 1-9, find the indefinite integral....Ch. 5.3 - In Exercises 1-9, find the indefinite integral....Ch. 5.3 - In Exercises 1-9, find the indefinite integral....Ch. 5.3 - In Exercises 1-9, find the indefinite integral....Ch. 5.3 - In Exercises 1-9, find the indefinite integral....Ch. 5.3 - In Exercises 1-9, find the indefinite integral....Ch. 5.3 - In Exercises 1-9, find the indefinite integral....Ch. 5.3 - In Exercises 1-9, find the indefinite integral....Ch. 5.3 - In Exercises 1-9, find the indefinite integral....Ch. 5.3 - In Exercises 10 and 11, find the particular...Ch. 5.3 - In Exercises 10 and 11, find the particular...Ch. 5.3 - The marginal cost of producing x units of a...Ch. 5.3 - Find an equation of the function f whose graph...Ch. 5.3 - The number of bolts B produced by a foundry...Ch. 5.3 - In Exercises 1520, find the indefinite integral....Ch. 5.3 - In Exercises 1520, find the indefinite integral....Ch. 5.3 - In Exercises 1520, find the indefinite integral....Ch. 5.3 - In Exercises 1520, find the indefinite integral....Ch. 5.3 - In Exercises 1520, find the indefinite integral....Ch. 5.3 - In Exercises 1520, find the indefinite integral....Ch. 5.3 - The rate of change in revenue for Under Armour...Ch. 5.4 - Checkpoint 1 Worked-out solution available at...Ch. 5.4 - Checkpoint 2 Worked-out solution available at...Ch. 5.4 - Checkpoint 3 Worked-out solution available at...Ch. 5.4 - Checkpoint 4 Worked-out solution available at...Ch. 5.4 - Checkpoint 5 Worked-out solution available at...Ch. 5.4 - Checkpoint 6 Worked-out solution available at...Ch. 5.4 - Checkpoint 7 Worked-out solution available at...Ch. 5.4 - Checkpoint 8 Worked-out solution available at...Ch. 5.4 - Checkpoint 9 Worked-out solution available at...Ch. 5.4 - In Exercises 1-4, find the indefinite integral....Ch. 5.4 - In Exercises 1-4, find the indefinite integral....Ch. 5.4 - In Exercises 1-4, find the indefinite integral....Ch. 5.4 - In Exercises 1-4, find the indefinite integral....Ch. 5.4 - In Exercises 5-7, integrate the marginal function....Ch. 5.4 - In Exercises 5-7, integrate the marginal function....Ch. 5.4 - In Exercises 5-7, integrate the marginal function....Ch. 5.4 - Evaluating a Definite integral using a Geometric...Ch. 5.4 - Evaluating a Definite integral using a Geometric...Ch. 5.4 - Evaluating a Definite integral using a Geometric...Ch. 5.4 - Evaluating a Definite integral using a Geometric...Ch. 5.4 - Evaluating a Definite integral using a Geometric...Ch. 5.4 - Evaluating a Definite Integral Using a Geometric...Ch. 5.4 - Using Properties of Definite Integrals In...Ch. 5.4 - Using Properties of Definite Integrals In...Ch. 5.4 - Finding Area by the Fundamental Theorem In...Ch. 5.4 - Finding Area by the Fundamental Theorem In...Ch. 5.4 - Finding Area by the Fundamental Theorem In...Ch. 5.4 - Finding Area by the Fundamental Theorem In...Ch. 5.4 - Finding Area by the Fundamental Theorem In...Ch. 5.4 - Finding Area by the Fundamental Theorem In...Ch. 5.4 - Finding Area by the Fundamental Theorem In...Ch. 5.4 - Finding Area by the Fundamental Theorem In...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 17-38,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 1738,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 1738,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 1738,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 1738,...Ch. 5.4 - Definite Integral Involving Absolute Value In...Ch. 5.4 - Definite Integral Involving Absolute Value In...Ch. 5.4 - Definite Integral Involving Absolute Value In...Ch. 5.4 - Definite Integral Involving Absolute Value In...Ch. 5.4 - Finding the Area of a Region In Exercises 43-46,...Ch. 5.4 - Finding the Area of a Region In Exercises 43-46,...Ch. 5.4 - Finding the Area of a Region In Exercises 43-46,...Ch. 5.4 - Finding the Area of a Region In Exercises 43-46,...Ch. 5.4 - Marginal Analysis In Exercises 4752, find the...Ch. 5.4 - Marginal Analysis In Exercises 4752, find the...Ch. 5.4 - Marginal Analysis In Exercises 4752, find the...Ch. 5.4 - Marginal Analysis In Exercises 4752, find the...Ch. 5.4 - Marginal Analysis In Exercises 4752, find the...Ch. 5.4 - Marginal Analysis In Exercises 4752, find the...Ch. 5.4 - Average Value of a Function In Exercises 53-60,...Ch. 5.4 - Average Value of a Function In Exercises 53-60,...Ch. 5.4 - Average Value of a Function In Exercises 53-60,...Ch. 5.4 - Average Value of a Function In Exercises 5360,...Ch. 5.4 - Average Value of a Function In Exercises 53-60,...Ch. 5.4 - Average Value of a Function In Exercises 53-60,...Ch. 5.4 - Average Value of a Function In Exercises 53-60,...Ch. 5.4 - Average Value of a Function In Exercises 53-60,...Ch. 5.4 - Integrating Even and Odd Functions In Exercises...Ch. 5.4 - Integrating Even and Odd Functions In Exercises...Ch. 5.4 - Integrating Even and Odd Functions In Exercises...Ch. 5.4 - Integrating Even and Odd Functions In Exercises...Ch. 5.4 - Using Properties of Definite Integrals Use the...Ch. 5.4 - Using Properties of Definite Integrals Use the...Ch. 5.4 - Finding the Amount of an Annuity In Exercises...Ch. 5.4 - Finding the Amount of an Annuity In Exercises...Ch. 5.4 - Finding the Amount of an Annuity In Exercises...Ch. 5.4 - Finding the Amount of an Annuity In Exercises...Ch. 5.4 - Capital Accumulation In Exercises 71-74, you are...Ch. 5.4 - Capital Accumulation In Exercises 71-74, you are...Ch. 5.4 - Capital Accumulation In Exercises 71-74, you are...Ch. 5.4 - Capital Accumulation In Exercises 71-74, you are...Ch. 5.4 - Cost The total cost of purchasing a piece of...Ch. 5.4 - Depreciation A company purchases a new machine for...Ch. 5.4 - Compound Interest A deposit of $2250 is made in a...Ch. 5.4 - HOW DO YOU SEE IT? A college graduate has two job...Ch. 5.4 - Mortgage Debt The rate of change of mortgage debt...Ch. 5.5 - Checkpoint 1 Worked-out solution available at...Ch. 5.5 - Checkpoint 2 Worked-out solution available at...Ch. 5.5 - Checkpoint 3 Worked-out solution available at...Ch. 5.5 - Checkpoint 4 Worked-out solution available at...Ch. 5.5 - Checkpoint 5 Worked-out solution available at...Ch. 5.5 - Checkpoint 6 Worked-out solution available at...Ch. 5.5 - In Exercises 1-4, simplify the expression....Ch. 5.5 - In Exercises 1-4, simplify the expression....Ch. 5.5 - In Exercises 1-4, simplify the expression....Ch. 5.5 - In Exercises 1-4, simplify the expression....Ch. 5.5 - In Exercises 5-8, find the points of intersection...Ch. 5.5 - In Exercises 5-8, find the points of intersection...Ch. 5.5 - In Exercises 5-8, find the points of intersection...Ch. 5.5 - In Exercises 5-8, find the points of intersection...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Region In Exercises 9-12, the...Ch. 5.5 - Finding the Region In Exercises 9-12, the...Ch. 5.5 - Finding the Region In Exercises 9-12, the...Ch. 5.5 - Finding the Region In Exercises 9-12, the...Ch. 5.5 - Think About It In Exercises 13 and 14, determine...Ch. 5.5 - Think About It In Exercises 13 and 14, determine...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Finding the Area Bounded by Two Graphs In...Ch. 5.5 - Writing Integrals In Exercises 31-34, use a...Ch. 5.5 - Writing Integrals In Exercises 31-34, use a...Ch. 5.5 - Writing Integrals In Exercises 31-34, use a...Ch. 5.5 - Writing Integrals In Exercises 31-34, use a...Ch. 5.5 - Finding Area In Exercises 35-40, use a graphing...Ch. 5.5 - Finding Area In Exercises 35-40, use a graphing...Ch. 5.5 - Finding Area In Exercises 35-40, use a graphing...Ch. 5.5 - Finding Area In Exercises 35-40, use a graphing...Ch. 5.5 - Finding Area In Exercises 35-40, use a graphing...Ch. 5.5 - Finding Area In Exercises 35-40, use a graphing...Ch. 5.5 - Area of a Region In Exercises 41 and 42, use...Ch. 5.5 - Area of a Region In Exercises 41 and 42, use...Ch. 5.5 - Consumer and Producer Surpluses In Exercises...Ch. 5.5 - Consumer and Producer Surpluses In Exercises...Ch. 5.5 - Consumer and Producer Surpluses In Exercises...Ch. 5.5 - Consumer and Producer Surpluses In Exercises...Ch. 5.5 - Consumer and Producer Surpluses In Exercises...Ch. 5.5 - Consumer and Producer Surpluses In Exercises...Ch. 5.5 - Revenue In Exercises 49 and 50, two models, R1 and...Ch. 5.5 - Revenue In Exercises 49 and 50, two models, R1 and...Ch. 5.5 - Fuel Cost The projected fuel cost C (in millions...Ch. 5.5 - Health An epidemic was spreading such that t weeks...Ch. 5.5 - Consumer Trends For the years 2003 through 2012,...Ch. 5.5 - HOW DO YOU SEE IT? A state legislature is debating...Ch. 5.5 - Cost, Revenue, and Profit The revenue (in millions...Ch. 5.5 - Cost, Revenue, and Profit Repeat Exercise 55 for...Ch. 5.5 - Consumer and Producer Surpluses Factory orders for...Ch. 5.5 - Consumer and Producer Surpluses Repeat Exercise 57...Ch. 5.6 - Checkpoint 1 Worked-out solution available at...Ch. 5.6 - Checkpoint 2 Worked-out solution available at...Ch. 5.6 - Checkpoint 3 Worked-out solution available at...Ch. 5.6 - In Exercises 1-6, find the midpoint of the...Ch. 5.6 - In Exercises 1-6, find the midpoint of the...Ch. 5.6 - In Exercises 1-6, find the midpoint of the...Ch. 5.6 - In Exercises 1-6, find the midpoint of the...Ch. 5.6 - In Exercises 1-6, find the midpoint of the...Ch. 5.6 - In Exercises 1-6, find the midpoint of the...Ch. 5.6 - In Exercises 7-10, find the limit....Ch. 5.6 - In Exercises 7-10, find the limit. limx4x+57x5Ch. 5.6 - In Exercises 7-10, find the limit. limxx7x2+1Ch. 5.6 - In Exercises 7-10, find the limit....Ch. 5.6 - Approximating the Area of a Plane Region In...Ch. 5.6 - Approximating the Area of a Plane Region In...Ch. 5.6 - Approximating the Area of a Plane Region In...Ch. 5.6 - Approximating the Area of a Plane Region In...Ch. 5.6 - Approximating the Area of a Plane Region In...Ch. 5.6 - Approximating the Area of a Plane Region In...Ch. 5.6 - Using the Midpoint Rule In Exercises 7-14, use the...Ch. 5.6 - Using the Midpoint Rule In Exercises 7-14, use the...Ch. 5.6 - Using the Midpoint Rule In Exercises 7-14, use the...Ch. 5.6 - Using the Midpoint Rule In Exercises 7-14, use the...Ch. 5.6 - Using the Midpoint Rule In Exercises 7-14, use the...Ch. 5.6 - Using the Midpoint Rule In Exercises 7-14, use the...Ch. 5.6 - Using the Midpoint Rule In Exercises 7-14, use the...Ch. 5.6 - Using the Midpoint Rule In Exercises 7-14, use the...Ch. 5.6 - Using the Midpoint Rule In Exercises 15-20, use...Ch. 5.6 - Using the Midpoint Rule In Exercises 15-20, use...Ch. 5.6 - Using the Midpoint Rule In Exercises 15-20, use...Ch. 5.6 - Using the Midpoint Rule In Exercises 15-20, use...Ch. 5.6 - Using the Midpoint Rule In Exercises 15-20, use...Ch. 5.6 - Using the Midpoint Rule In Exercises 15-20, use...Ch. 5.6 - Surface Area Use the Midpoint Rule to estimate the...Ch. 5.6 - Surface Area Use the Midpoint Rule to estimate the...Ch. 5.6 - Surface Area Use the Midpoint Rule to estimate the...Ch. 5.6 - Numerical Approximation Use the Midpoint Rule with...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding Indefinite Integrals In Exercises 114,...Ch. 5 - Finding a Particular Solution In Exercises 1518,...Ch. 5 - Finding a Particular Solution In Exercises 1518,...Ch. 5 - Finding a Particular Solution In Exercises 1518,...Ch. 5 - Finding a Particular Solution In Exercises 1518,...Ch. 5 - Vertical Motion An object is projected upward from...Ch. 5 - Revenue A company produces a new product for which...Ch. 5 - Applying the General Power Rule In Exercises 2132,...Ch. 5 - Applying the General Power Rule In Exercises 2132,...Ch. 5 - Applying the General Power Rule In Exercises 2132,...Ch. 5 - Applying the General Power Rule In Exercises 2132,...Ch. 5 - Applying the General Power Rule In Exercises 2132,...Ch. 5 - Applying the General Power Rule In Exercises 2132,...Ch. 5 - Applying the General Power Rule In Exercises 2132,...Ch. 5 - Applying the General Power Rule In Exercises 2132,...Ch. 5 - Applying the General Power Rule In Exercises 2132,...Ch. 5 - Applying the General Power Rule In Exercises 2132,...Ch. 5 - Applying the General Power Rule In Exercises 2132,...Ch. 5 - Applying the General Power Rule In Exercises 2132,...Ch. 5 - Production The rate of change of the output of a...Ch. 5 - Cost The marginal cost for a catering service to...Ch. 5 - Using the Exponential and Log Rules In Exercises...Ch. 5 - Using the Exponential and Log Rules In Exercises...Ch. 5 - Using the Exponential and Log Rules In Exercises...Ch. 5 - Using the Exponential and Log Rules In Exercises...Ch. 5 - Using the Exponential and Log Rules In Exercises...Ch. 5 - Using the Exponential and Log Rules In Exercises...Ch. 5 - Using the Exponential and Log Rules In Exercises...Ch. 5 - Using the Exponential and Log Rules In Exercises...Ch. 5 - Using the Exponential and Log Rules In Exercises...Ch. 5 - Using the Exponential and Log Rules In Exercises...Ch. 5 - Using the Exponential and Log Rules In Exercises...Ch. 5 - Using the Exponential and Log Rules In Exercises...Ch. 5 - Evaluating a Definite Integral using a Geometric...Ch. 5 - Evaluating a Definite Integral using a Geometric...Ch. 5 - Evaluating a Definite Integral using a Geometric...Ch. 5 - Evaluating a Definite Integral using a Geometric...Ch. 5 - Using Properties of Definite integrals Given...Ch. 5 - Using Properties of Definite Integrals Given...Ch. 5 - Finding Area by the Fundamental Theorem In...Ch. 5 - Finding Area by the Fundamental Theorem In...Ch. 5 - Finding Area by the Fundamental Theorem In...Ch. 5 - Finding Area by the Fundamental Theorem In...Ch. 5 - Finding Area by the Fundamental Theorem In...Ch. 5 - Finding Area by the Fundamental Theorem In...Ch. 5 - Evaluating a Definite Integral In Exercises 5970,...Ch. 5 - Evaluating a Definite Integral In Exercises 5970,...Ch. 5 - Evaluating a Definite Integral In Exercises 5970,...Ch. 5 - Evaluating a Definite Integral In Exercises 5970,...Ch. 5 - Evaluating a Definite Integral In Exercises 5970,...Ch. 5 - Evaluating a Definite Integral In Exercises 5970,...Ch. 5 - Evaluating a Definite Integral In Exercises 5970,...Ch. 5 - Evaluating a Definite Integral In Exercises 5970,...Ch. 5 - Evaluating a Definite Integral In Exercises 5970,...Ch. 5 - Evaluating a Definite Integral In Exercises 5970,...Ch. 5 - Evaluating a Definite Integral In Exercises 5970,...Ch. 5 - Evaluating a Definite Integral In Exercises 5970,...Ch. 5 - Average Value of a Function In Exercises 7176,...Ch. 5 - Average Value of a Function In Exercises 7176,...Ch. 5 - Average Value of a Function In Exercises 71-76,...Ch. 5 - Average Value of a Function In Exercises 7176,...Ch. 5 - Average Value of a Function In Exercises 7176,...Ch. 5 - Average Value of a Function In Exercises 7176,...Ch. 5 - Integrating Even and Odd Functions In Exercises...Ch. 5 - Integrating Even and Odd Functions In Exercises...Ch. 5 - Integrating Even and Odd Functions In Exercises...Ch. 5 - Integrating Even and Odd Functions In Exercises...Ch. 5 - Finding the Amount of an Annuity In Exercises 81...Ch. 5 - Finding the Amount of an Annuity In Exercises 81...Ch. 5 - Cost The marginal cost of serving an additional...Ch. 5 - Profit The marginal profit obtained by selling x...Ch. 5 - Compound Interest A deposit of $500 is made in a...Ch. 5 - Sales The rate of change in sales for Garmin from...Ch. 5 - Finding the Area Bounded by Two Graphs In...Ch. 5 - Finding the Area Bounded by Two Graphs In...Ch. 5 - Finding the Area Bounded by Two Graphs In...Ch. 5 - Finding the Area Bounded by Two Graphs In...Ch. 5 - Finding the Area Bounded by Two Graphs In...Ch. 5 - Finding the Area Bounded by Two Graphs In...Ch. 5 - Finding the Area Bounded by Two Graphs In...Ch. 5 - Finding the Area Bounded by Two Graphs In...Ch. 5 - Consumer and Producer Surpluses In Exercises...Ch. 5 - Consumer and Producer Surpluses In Exercises...Ch. 5 - Consumer and Producer Surpluses In Exercises...Ch. 5 - Consumer and Producer Surpluses In Exercises...Ch. 5 - Revenue For the years 2020 through 2025, two...Ch. 5 - Revenue For the years 2004 through 2013, the...Ch. 5 - Cost, Revenue, and Profit The revenue (in millions...Ch. 5 - Cost, Revenue, and Profit Repeat Exercise 101 for...Ch. 5 - Approximating the Area of a Plane Region In...Ch. 5 - Approximating the Area of a Plane Region In...Ch. 5 - Using the Midpoint Rule In Exercises 105-110, use...Ch. 5 - Using the Midpoint Rule In Exercises 105-110, use...Ch. 5 - Using the Midpoint Rule In Exercises 105-110, use...Ch. 5 - Using the Midpoint Rule In Exercises 105-110, use...Ch. 5 - Using the Midpoint Rule In Exercises 105-110, use...Ch. 5 - Using the Midpoint Rule In Exercises 105-110, use...Ch. 5 - Using the Midpoint Rule In Exercises 111-114, use...Ch. 5 - Using the Midpoint Rule In Exercises 111-114, use...Ch. 5 - Using the Midpoint Rule In Exercises 111-114, use...Ch. 5 - Using the Midpoint Rule In Exercises 111-114, use...Ch. 5 - Surface Area Use the Midpoint Rule to estimate the...Ch. 5 - Take this test as you would take a test in class....Ch. 5 - Take this test as you would take a test in class....Ch. 5 - Take this test as you would take a test in class....Ch. 5 - Take this test as you would take a test in class....Ch. 5 - Take this test as you would take a test in class....Ch. 5 - Take this test as you would take a test in class....Ch. 5 - In Exercises 7 and 8, find the particular solution...Ch. 5 - In Exercises 7 and 8, find the particular solution...Ch. 5 - In Exercises 9-14, evaluate the definite integral....Ch. 5 - In Exercises 9-14, evaluate the definite integral....Ch. 5 - In Exercises 9-14, evaluate the definite integral....Ch. 5 - In Exercises 9-14, evaluate the definite integral....Ch. 5 - In Exercises 9-14, evaluate the definite integral....Ch. 5 - In Exercises 9-14, evaluate the definite integral....Ch. 5 - The rate of change in sales of Ross Stores from...Ch. 5 - In Exercises 16-19, sketch the region bounded by...Ch. 5 - In Exercises 16-19, sketch the region bounded by...Ch. 5 - In Exercises 16-19, sketch the region bounded by...Ch. 5 - In Exercises 16-19, sketch the region bounded by...Ch. 5 - The demand and supply functions for a product are...Ch. 5 - In Exercises 21 and 22, use the Midpoint Rule with...Ch. 5 - In Exercises 21 and 22, use the Midpoint Rule with...

Find more solutions based on key concepts

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Finite Mathematics and Applied Calculus (MindTap Course List)

Comet Hale-Bopp, discovered in 1995, has an elliptical orbit with eccentricity 0.9951. The length of the orbits...

Calculus: Early Transcendentals

Use Stokes Theorem to evaluate c F dr. In each Case C is oriented counterclockwise as viewed from above. 10. F...

Multivariable Calculus

Finding a Limit In Exercises 11-28, find the limit. limx6x2

Calculus: Early Transcendental Functions

Evaluate the integral. 55edx

Single Variable Calculus: Early Transcendentals, Volume I

Add or Subtract Perform the addition or subtraction and simplify. 54. xx2+x22x25x+4

Precalculus: Mathematics for Calculus (Standalone Book)

The following scores are the ages for a random sample of n = 32 drivers who were issued parking tickets in Chic...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

For a math test on which the mean score was 59 and the standard deviation was 4, what is the probability that a...

Essentials Of Statistics

a Prove that sin1x+cos1x=/2 b Use part a to prove Formula 6.

Calculus (MindTap Course List)

In Exercises 75-98, perform the indicated operations and/or simplify each expression. 97. 100(10te0.1t 100e0.1...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

A population of N = 15 scores has SX = 120. What is the population mean?

Statistics for The Behavioral Sciences (MindTap Course List)

Application Using the software or calculator available to you, do the following: 1. Trade winds are one of the ...

Understanding Basic Statistics

Find the domain of the function. 31. f(x)=x+4x29

Single Variable Calculus

In problems 23-58, perform the indicated operations and simplify.
49.

Mathematical Applications for the Management, Life, and Social Sciences

Simplify the expressions in Exercises 5764, given that x,y,z,a,b, and c are positive real numbers. (x+9)2

Finite Mathematics

Verify a Conjecture Use deductive reasoning to show that the following procedure always produces a number that ...

Mathematical Excursions (MindTap Course List)

An insurance company offers four different deductible levelsnone, low, medium, and highfor its homeowners polic...

Probability and Statistics for Engineering and the Sciences

For Problems 1-10, answer true or false. The statement |64|=|46| is a true statement.

Intermediate Algebra

Temperature readings T (in F) were recorded every two hours from midnight to 2:00 PM in Atlanta on June 4, 2013...

Single Variable Calculus: Early Transcendentals

Round the following numbers to the indicated place.
13. 4.6935 to tenths

Contemporary Mathematics for Business & Consumers

Find the number of sides of a regular polygon that has a central angle measuring a 90. c 60. b 45. d 24.

Elementary Geometry For College Students, 7e

Force Tyler and his cousin Kelly have attached a rope to the branch of a tree and tied a board to the other end...

Trigonometry (MindTap Course List)

Let H1 and H2 be cyclic subgroups of the abelian group G, where H1H2=0. Prove that H1H2 is cyclic if and only i...

Elements Of Modern Algebra

Simplify by first removing the parentheses and then combining the like terms: 6(2a+8b)

Elementary Technical Mathematics

Finding an Inverse Function In 63-68, (a) sketch a graph of the function f, (b) determine an interval on which ...

Calculus: Early Transcendental Functions (MindTap Course List)

Evaluating Trigonometric Functions In Exercises 65-70, evaluate the sine, cosine, and tangent of the angle. Do ...

Calculus of a Single Variable

Let E and F be two events, and suppose that P(E)=.35, P(F)=.55, and P(EF)=.70. Find P(E|F).

Finite Mathematics for the Managerial, Life, and Social Sciences

The perimeter of the rectangle is 32 cm. Where x is the width and y is the length, express the area A of the re...

Elementary Geometry for College Students

Find for .

Study Guide for Stewart's Multivariable Calculus, 8th

A definite integral for the area shaded at the right is: a) 0/2(sinxx)dx b) 0/2(sinx+x)dx c) 01(sinxx)dx d) 01(...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Finding Intercepts In Exercises 19-28, find any intercepts. y2=x34x

Calculus (MindTap Course List)

Using the Three-Dimensional Coordinate SystemIn Exercises 1324, determine the location of a point (x,y,z) that ...

Multivariable Calculus

A survey of high school students is described in the report Students on STEM (changetheequation.org/students-st...

Introduction To Statistics And Data Analysis

Finding Percentage, Percent, and Base in Practical Applications Solve the following problems. 16. How many poun...

Mathematics For Machine Technology

Describe the appearance of a scatter plot showing the data from a set of scores that produce a Pearson correlat...

Research Methods for the Behavioral Sciences (MindTap Course List)

Decompose each fraction into partial fractions. -2x+11x2-x-6

College Algebra (MindTap Course List)

A sample of 15 consumers provided the following product ratings for three different products. Five consumers we...

Statistics for Business & Economics, Revised (MindTap Course List)

Refer to exercise 9, where the following data were used to investigate the relationship between the number of c...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe the structure of a multiple-baseline design and explain how the results from this design can demonstra...

Research Methods for the Behavioral Sciences (MindTap Course List)

For how many integers from 1 through 99,999 is the sum of their digits equal to 10?

Discrete Mathematics With Applications

Refer to the data in exercise 28. Consider a model in which only Industry is used to predict Delay. At a .01 le...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

In Exercises4754, find the probability that the sum is as states when a pair of dice is rolled. a. even and les...

Mathematics: A Practical Odyssey

Answer Problems 110 without referring back to the text. Fill in the blank or answer true or false. 7. If y = c1...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

The following data are from matched samples taken from two populations.
Compute the difference value for each ...

Essentials Of Statistics For Business & Economics

HomogeneityExercises S-7 through S-I3 deal with the homogeneity property. Let f(x)=cx2.53. By what factor x be...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Finding the Area of a Triangle: In Exercises 15-18, use a determinant to find the area of the triangle with the...

College Algebra

[T] Use a computer algebra system to compute the Riemann sum, LN, for N = 10. 30, 50 for f(x)=1x2 on [1, 1].

Calculus Volume 2