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10th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285057095

Chapter 5.8, Problem 88E

Textbook Problem

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Differential Equation In Exercises 87–90, solve the differential equation.

To determine

**To calculate:** The solution of the differential equation,

**Given:**

The differential equation is

**Formula used:**

Trigonometric identity,

And,

The integration of

Derivative of

**Calculation:**

Consider the given differential equation,

Simplify the equation as,

Now, integrate both side and simplify as,

Now, put

Now use these values in the above integral and simplify it as,

Calculus

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Prove...Ch. 5.3 - Proof Prove that if f has an inverse function,...Ch. 5.3 - Proof Prove that if a function has an inverse...Ch. 5.3 - Proof Prove that a function has an inverse...Ch. 5.3 - Using Theorem 5.7 Is the converse of the second...Ch. 5.3 - Derivative of an Inverse Function Show that...Ch. 5.3 - Derivative of an Inverse FunctionShow that...Ch. 5.3 - Derivative of an Inverse FunctionShow that...Ch. 5.3 - Inverse Function Let f(x)=x2x1 Show that f is its...Ch. 5.3 - Using a Function Let f(x)=ax+bcx+d (a) Show that f...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Sketching a Graph In Exercises 19-24, sketch the...Ch. 5.4 - Sketching a Graph In Exercises 17-22, sketch the...Ch. 5.4 - Sketching a Graph In Exercises 17-22, sketch the...Ch. 5.4 - Sketching a Graph In Exercises 17-22, sketch the...Ch. 5.4 - Sketching a Graph In Exercises 19-24, sketch the...Ch. 5.4 - Sketching a Graph In Exercises 19-24, sketch the...Ch. 5.4 - 23. Comparing Graphs Use a graphing utility to...Ch. 5.4 - Asymptotes Use a graphing utility to graph the...Ch. 5.4 - Matching In Exercises 2528, match the equation...Ch. 5.4 - Matching In Exercises 2528, match the equation...Ch. 5.4 - Matching In Exercises 2528, match the equation...Ch. 5.4 - Matching In Exercises 2528, match the equation...Ch. 5.4 - Inverse Functions In Exercises 29-32, illustrate...Ch. 5.4 - Inverse Functions In Exercises 2932, illustrate...Ch. 5.4 - Inverse Functions In Exercises 2932, illustrate...Ch. 5.4 - Inverse Functions In Exercises 2932, illustrate...Ch. 5.4 - Finding a Derivative In Exercises 3354, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Implicit Differentiation In Exercises 63 and 64,...Ch. 5.4 - Implicit Differentiation In Exercises 63 and 64,...Ch. 5.4 - Finding the Equation of a Tangent Line In...Ch. 5.4 - Finding the Equation of a Tangent Line In...Ch. 5.4 - Finding a Second Derivative In Exercises 67 and...Ch. 5.4 - Finding a Second Derivative In Exercises 67 and...Ch. 5.4 - Differential Equation In Exercises 69 and 70, show...Ch. 5.4 - Differential Equation In Exercises 69 and 70, show...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Finding Extrema and Points of Inflection In...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Area Find the area of the largest rectangle that...Ch. 5.4 - Area Perform the following steps to find the...Ch. 5.4 - Finding an Equation of a Tangent Line Find point...Ch. 5.4 - HOW DO YOU SEE IT? The figure shows the graphs of...Ch. 5.4 - Depreciation The value V of an item t years after...Ch. 5.4 - Harmonic Motion The displacement from equilibrium...Ch. 5.4 - Atmospheric Pressure A meteorologist measures the...Ch. 5.4 - Modeling Data The table lists the approximate...Ch. 5.4 - Linear and Quadratic Approximation In Exercises 87...Ch. 5.4 - Linear and Quadratic Approximation In Exercises 87...Ch. 5.4 - Stirlings Formula For large values of n,...Ch. 5.4 - Stirling's Formula For large values of n, n! = 1 ...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite IntegralIn Exercises 91108,...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite IntegralIn Exercises 91108,...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite IntegralIn Exercises 109118,...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Slope Field In Exercises 119 and 120, a...Ch. 5.4 - Slope FieldIn Exercises 119 and 120, a...Ch. 5.4 - Differential Equation In Exercises 121 and 122,...Ch. 5.4 - Differential Equation In Exercises 119 and 120,...Ch. 5.4 - Differential Equation In Exercises 121 and 122,...Ch. 5.4 - Differential Equation In Exercises 121 and 122,...Ch. 5.4 - AreaIn Exercises 125128, find the area of the...Ch. 5.4 - Area In Exercises 123-126, find the area of the...Ch. 5.4 - Area In Exercises 123-126, find the area of the...Ch. 5.4 - Area In Exercises 123-126, find the area of the...Ch. 5.4 - Midpoint Rule In Exercises 127 and 128, use the...Ch. 5.4 - Midpoint Rule In Exercises 127 and 128, use the...Ch. 5.4 - Probability A car battery has an average lifetime...Ch. 5.4 - Probability The median waiting time (in minutes)...Ch. 5.4 - Modeling Data A valve on a storage tank is opened...Ch. 5.4 - Using the Area of a Region Find the value of a...Ch. 5.4 - WRITING ABOUT CONCEPTS Properties of the Natural...Ch. 5.4 - A Function and Its Derivative Is there a function...Ch. 5.4 - Choosing a Function Without integrating, state the...Ch. 5.4 - Analyzing a Graph Consider the function...Ch. 5.4 - Deriving an Inequality Given ex1 for x0, it...Ch. 5.4 - 141. Horizontal Motion The position function of a...Ch. 5.4 - Analyzing a Function Let f(x)=lnxx. (a) Graph f on...Ch. 5.4 - Solving an Equation Find, to three decimal places,...Ch. 5.4 - Finding the Maximum Rate of Change Verify that the...Ch. 5.5 - Evaluating a Logarithmic Expression In Exercises...Ch. 5.5 - Evaluating a Logarithmic Expression In Exercises...Ch. 5.5 - Evaluating a Logarithmic Expression In Exercises...Ch. 5.5 - Evaluating a Logarithmic Expression In Exercises...Ch. 5.5 - Exponential and Logarithmic Forms of Equations In...Ch. 5.5 - Exponential and Logarithmic Forms of Equations In...Ch. 5.5 - Exponential and Logarithmic Forms of Equations In...Ch. 5.5 - Exponential and Logarithmic Forms of Equations In...Ch. 5.5 - Sketching a Graph In Exercises 15-20, sketch the...Ch. 5.5 - Sketching a Graph In Exercises 15-20, sketch the...Ch. 5.5 - Sketching a Graph In Exercises 15-20, sketch the...Ch. 5.5 - Sketching a Graph In Exercises 15-20, sketch the...Ch. 5.5 - Sketching a Graph In Exercises 15-20, sketch the...Ch. 5.5 - Sketching a Graph In Exercises 15-20, sketch the...Ch. 5.5 - Matching In Exercises 15–18, match the function...Ch. 5.5 - MatchingIn Exercises 1518, match the function with...Ch. 5.5 - MatchingIn Exercises 1518, match the function with...Ch. 5.5 - Matching In Exercises 15–18, match the function...Ch. 5.5 - Solving an Equation In Exercises 21-26, solve for...Ch. 5.5 - Solving an Equation In Exercises 21-26, solve for...Ch. 5.5 - Solving an Equation In Exercises 21-26, solve for...Ch. 5.5 - Solving an Equation In Exercises 19–24, solve for...Ch. 5.5 - Solving an Equation In Exercises 21-26, solve for...Ch. 5.5 - Solving an Equation In Exercises 21-26, solve for...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 25–34, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 2534, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Inverse Functions In Exercises 37 and 38,...Ch. 5.5 - Inverse Functions In Exercises 37 and 38,...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 37-58, find the...Ch. 5.5 - Finding a Derivative In Exercises 37-58, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 37-58, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Logarithmic Differentiation In Exercises 65-68,...Ch. 5.5 - Logarithmic Differentiation In Exercises 65-68,...Ch. 5.5 - Logarithmic Differentiation In Exercises 65-68,...Ch. 5.5 - Logarithmic Differentiation In Exercises 65-68,...Ch. 5.5 - Finding an Equation of a Tangent LineIn Exercises...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 71–78,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 7178,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Evaluating a Definite Integral In Exercises 77-80,...Ch. 5.5 - Evaluating a Definite Integral In Exercises 77-80,...Ch. 5.5 - Evaluating a Definite Integral In Exercises 77-80,...Ch. 5.5 - Evaluating a Definite Integral In Exercises 7982,...Ch. 5.5 - Area In Exercises 83 and 84, find the area of the...Ch. 5.5 - Area In Exercises 83 and 84, find the area of the...Ch. 5.5 - Analyzing a Logarithmic Equation Consider the...Ch. 5.5 - Comparing Rates of Growth Order the functions...Ch. 5.5 - Inflation When the annual rate of inflation...Ch. 5.5 - Depreciation After t years, the value of a car...Ch. 5.5 - Compound Interest In Exercises 89-92, complete the...Ch. 5.5 - Compound Interest In Exercises 89-92, complete the...Ch. 5.5 - Compound Interest In Exercises 89–92, complete the...Ch. 5.5 - Compound Interest In Exercises 89-92, complete the...Ch. 5.5 - Compound Interest In Exercises 93–96, complete the...Ch. 5.5 - Compound Interest In Exercises 9396, complete the...Ch. 5.5 - Compound Interest In Exercises 93-96, complete the...Ch. 5.5 - Compound Interest In Exercises 93-96, complete the...Ch. 5.5 - Compound Interest Assume that you can earn 6% on...Ch. 5.5 - Compound Interest Consider a deposit of $100...Ch. 5.5 - Timber Yield The yield V (in millions of cubic...Ch. 5.5 - HOW DO YOU SEE IT? The graph shows the proportion...Ch. 5.5 - Population Growth A lake is stocked with 500 fish,...Ch. 5.5 - Modeling Data The breaking strengths B (in tons)...Ch. 5.5 - 103. Comparing Models The numbers y of pancreas...Ch. 5.5 - An Approximation of e Complete the table to...Ch. 5.5 - Modeling Data In Exercises 105 and 106, find an...Ch. 5.5 - Modeling Data In Exercises 105 and 106, find an...Ch. 5.5 - Using Properties of Exponents In Exercises...Ch. 5.5 - Using Properties of Exponents In Exercises...Ch. 5.5 - Using Properties of Exponents In Exercises...Ch. 5.5 - Using Properties of Exponents In Exercises...Ch. 5.5 - True or False? In Exercises 111–116, determine...Ch. 5.5 - True or False? In Exercises 111116, determine...Ch. 5.5 - True or False? In Exercises 111116, determine...Ch. 5.5 - True or False? In Exercises 111116, determine...Ch. 5.5 - True or False? In Exercises 111116, determine...Ch. 5.5 - True or False? In Exercises 111116, determine...Ch. 5.5 - Comparing Functions (a) Show that (23)22(32). (b)...Ch. 5.5 - Finding an inverse Function Let f(x)=ax1ax+1. for...Ch. 5.5 - Logistic Differential Equation Show that solving...Ch. 5.5 - Using Properties of Exponents function f(x)=ax,...Ch. 5.5 - Tangent Lines (a) Determine y' given yx=xy. (b)...Ch. 5.5 - Which is greater (n)n+1 or (n+1)n where n8?Ch. 5.5 - Show that if x is positive, then loge(1+1x)11+xCh. 5.6 - Restricted Domain What is a restricted domain? Why...Ch. 5.6 - Finding Coordinates In Exercises 5 and 6,...Ch. 5.6 - Finding Coordinates In Exercises 5 and 6,...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Approximating Inverse Trigonometric Functions In...Ch. 5.6 - Approximating Inverse Trigonometric Functions In...Ch. 5.6 - Approximating Inverse Trigonometric Functions In...Ch. 5.6 - Approximating Inverse Trigonometric Functions In...Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Evaluating an Expression In Exercises 25-28,...Ch. 5.6 - Evaluating an Expression In Exercises 25-28,...Ch. 5.6 - Evaluating an Expression In Exercises 25-28,...Ch. 5.6 - Evaluating an Expression In Exercises 25-28,...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Simplifying an Expression Using a Right TriangleIn...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Solving an Equation In Exercises 37-40, solve the...Ch. 5.6 - Solving an Equation In Exercises 37-40, solve the...Ch. 5.6 - Solving an Equation In Exercises 37-40, solve the...Ch. 5.6 - Solving an Equation In Exercises 37-40, solve the...Ch. 5.6 - Verifying Identities In Exercises 81 and 82,...Ch. 5.6 - Verifying Identities In Exercises 81 and 82,...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.6 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.6 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.6 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.6 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.6 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.6 - Finding Relative Extrema In Exercises 63-66, find...Ch. 5.6 - Finding Relative Extrema In Exercises 63-66, find...Ch. 5.6 - Finding Relative Extrema In Exercises 63-66, find...Ch. 5.6 - Finding Relative Extrema In Exercises 63-66, find...Ch. 5.6 - Analyzing an Inverse Trigonometric Graph In...Ch. 5.6 - Analyzing an Inverse Trigonometric Graph In...Ch. 5.6 - Analyzing an Inverse Trigonometric Graph In...Ch. 5.6 - Analyzing an Inverse Trigonometric Graph In...Ch. 5.6 - Implicit Differentiation In Exercises 71-74, use...Ch. 5.6 - Implicit Differentiation In Exercises 71-74, use...Ch. 5.6 - Implicit Differentiation In Exercises 71-74, use...Ch. 5.6 - Implicit Differentiation In Exercises 71-74, use...Ch. 5.6 - Finding Values (a) Use a graphing utility to...Ch. 5.6 - HOW DO YOU SEE IT? The graph of g(x) = cos x is...Ch. 5.6 - Inverse Trigonometric Functions Explain why tan =0...Ch. 5.6 - True or False? In Exercises 83-86, determine...Ch. 5.6 - True or False? In Exercises 83-86, determine...Ch. 5.6 - True or False? In Exercises 83-86, determine...Ch. 5.6 - True or False? In Exercises 83-86, determine...Ch. 5.6 - True or False? In Exercises 8590, determine...Ch. 5.6 - True or False? In Exercises 8590, determine...Ch. 5.6 - Linear and Quadratic Approximations In Exercises...Ch. 5.6 - Linear and Quadratic Approximations In Exercises...Ch. 5.6 - Linear and Quadratic Approximations In Exercises...Ch. 5.6 - Linear and Quadratic Approximations In Exercises...Ch. 5.6 - Angular Rate of Change An airplane flies at an...Ch. 5.6 - Writing Repeat Exercise 87 for an altitude of 3...Ch. 5.6 - Angular Rate of Change In a free-fall experiment,...Ch. 5.6 - Angular Rate of Change A television camera at...Ch. 5.6 - Maximizing an Angle A billboard 85 feet wide is...Ch. 5.6 - Angular Speed A patrol car is parked 50 feet from...Ch. 5.6 - Proof (a) Prove that...Ch. 5.6 - Proof Prove each differentiation formula. (a)...Ch. 5.6 - Describing a Graph Use a graphing utility to graph...Ch. 5.6 - Think About It Use a graphing utility to graph...Ch. 5.6 - Maximizing an Angle In the figure, find the value...Ch. 5.6 - Finding a Distance In the figure, find PR such...Ch. 5.6 - Proof Prove that arcsinx=arctan(x1x2),x1.Ch. 5.6 - Inverse Secant Function Some calculus textbooks...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 120,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 120,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 120,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 120,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 2132,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 2334,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Completing the Square In Exercises 35-42, find or...Ch. 5.7 - Completing the Square In Exercises 3342, find or...Ch. 5.7 - Completing the Square In Exercises 3342, find or...Ch. 5.7 - Completing the Square In Exercises 3342, find or...Ch. 5.7 - Completing the Square In Exercises 35-42, find or...Ch. 5.7 - Completing the Square In Exercises 35-42, find or...Ch. 5.7 - Completing the Square In Exercises 35-42, find or...Ch. 5.7 - Completing the Square In Exercises 35-42, find or...Ch. 5.7 - Completing the Square In Exercises 3342, find or...Ch. 5.7 - Completing the Square In Exercises 3342, find or...Ch. 5.7 - Integration by Substitution In Exercises 43-46,...Ch. 5.7 - Integration by Substitution In Exercises 43-46,...Ch. 5.7 - Integration by Substitution In Exercises 43-46,...Ch. 5.7 - Integration by Substitution In Exercises 43-46,...Ch. 5.7 - Comparing Integration Problems In Exercises 47-50,...Ch. 5.7 - Comparing Integration Problems In Exercises 47-50,...Ch. 5.7 - Comparing Integration Problems In Exercises 47-50,...Ch. 5.7 - Comparing Integration Problems In Exercises 47-50,...Ch. 5.7 - Finding an Integral Decide whether you can find...Ch. 5.7 - HOW DO YOU SEE IT? Using the graph, which value...Ch. 5.7 - Differential Equation In Exercises 61 and 62, find...Ch. 5.7 - Differential Equation In Exercises 61 and 62, find...Ch. 5.7 - Slope Field In Exercises 55 and 56, a differential...Ch. 5.7 - Slope Field In Exercises 55 and 56, a differential...Ch. 5.7 - Slope Field In Exercises 57-60, use a graphing...Ch. 5.7 - Slope Field In Exercises 5760, use a graphing...Ch. 5.7 - Slope Field In Exercises 57-60, use a graphing...Ch. 5.7 - Slope Field In Exercises 57-60, use a graphing...Ch. 5.7 - Area In Exercises 63-66, find the area of the...Ch. 5.7 - Area In Exercises 63-66, find the area of the...Ch. 5.7 - Area In Exercises 6166, find the area of the...Ch. 5.7 - Area In Exercises 61–66, find the area of the...Ch. 5.7 - Area In Exercises 63-66, find the area of the...Ch. 5.7 - Area In Exercises 63-66, find the area of the...Ch. 5.7 - Area (a) Sketch the region whose area is...Ch. 5.7 - Approximating Pi (a) Show that 0141+x2dx= (b)...Ch. 5.7 - Investigation Consider the function...Ch. 5.7 - Comparing Integrals Consider the integral 16xx2dx...Ch. 5.7 - True or False? 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