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Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759
BuyFind

Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759

Solutions

Chapter
Section
Chapter 13.4, Problem 32E
Textbook Problem

Limits of Sequences If the sequence with the given nth term is convergent, find its limit. If it is divergent, explain why.

32. a n = 5 n ( n + 4 n [ n ( n + 1 ) 2 ] )

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Chapter 13 Solutions

Precalculus: Mathematics for Calculus (Standalone Book)
Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - One-Sided Limits Graph the piecewise-defined...Ch. 13.1 - One-Sided Limits Graph the piecewise-defined...Ch. 13.1 - One-Sided Limits Graph the piecewise-defined...Ch. 13.1 - One-Sided Limits Graph the piecewise-defined...Ch. 13.1 - DISCUSS: A Function with Specified Limits Sketch...Ch. 13.1 - DISCUSS: Graphing Calculator Pitfalls (a)...Ch. 13.2 - Suppose the following limits exist:...Ch. 13.2 - If f is a polynomial or a rational function and a...Ch. 13.2 - Limits from a Graph The graphs of f and g are...Ch. 13.2 - Using Limit Laws Suppose that...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Find the limit, and use a graphing...Ch. 13.2 - Finding Limits Find the limit, and use a graphing...Ch. 13.2 - Finding Limits Find the limit, and use a graphing...Ch. 13.2 - Finding Limits Find the limit, and use a graphing...Ch. 13.2 - Does the Limit Exist? Find the limit, if it...Ch. 13.2 - Does the Limit Exist? Find the limit, if it...Ch. 13.2 - Does the Limit Exist? Find the limit, if it...Ch. 13.2 - Does the Limit Exist? Find the limit, if it...Ch. 13.2 - Does the Limit Exist? Find the limit, if it...Ch. 13.2 - Does the Limit Exist? Find the limit, if it...Ch. 13.2 - Does the Limit Exist? Let f(x)={x1ifx2x24x+6ifx2...Ch. 13.2 - Does the Limit Exist? Let h(x)={xifx0x2if0x28xifx2...Ch. 13.2 - Finding Limits Numerically and Graphically (a)...Ch. 13.2 - Finding Limits Numerically and Graphically (a) Use...Ch. 13.2 - DISCUSS: Cancellation and Limits (a) What is wrong...Ch. 13.2 - DISCUSS: The Lorentz Contraction In the theory of...Ch. 13.2 - DISCUSS PROVE: Limits of Sums and Products (a)...Ch. 13.3 - The derivative of a function f at a number a is...Ch. 13.3 - If y = f(x), the average rate of change of f...Ch. 13.3 - Slope of a Tangent Line Find the slope of the...Ch. 13.3 - Slope of a Tangent Line Find the slope of the...Ch. 13.3 - Slope of a Tangent Line Find the slope of the...Ch. 13.3 - Slope of a Tangent Line Find the slope of the...Ch. 13.3 - Slope of a Tangent Line Find the slope of the...Ch. 13.3 - Slope of a Tangent Line Find the slope of the...Ch. 13.3 - Slope of a Tangent Line Find the slope of the...Ch. 13.3 - Slope of a Tangent Line Find the slope of the...Ch. 13.3 - Equation of a Tangent Line Find an equation of the...Ch. 13.3 - Equation of a Tangent Line Find an equation of the...Ch. 13.3 - Equation of a Tangent Line Find an equation of the...Ch. 13.3 - Equation of a Tangent Line Find an equation of the...Ch. 13.3 - Equation of a Tangent Line Find an equation of the...Ch. 13.3 - Equation of a Tangent Line Find an equation of the...Ch. 13.3 - Equation of a Tangent Line Find an equation of the...Ch. 13.3 - Equation of a Tangent Line Find an equation of the...Ch. 13.3 - The Derivative at a Number Find the derivative of...Ch. 13.3 - The Derivative at a Number Find the derivative of...Ch. 13.3 - The Derivative at a Number Find the derivative of...Ch. 13.3 - The Derivative at a Number Find the derivative of...Ch. 13.3 - The Derivative at a Number Find the derivative of...Ch. 13.3 - The Derivative at a Number Find the derivative of...Ch. 13.3 - The Derivative at a Number Find the derivative of...Ch. 13.3 - The Derivative at a Number Find the derivative of...Ch. 13.3 - Evaluating Derivatives Find the following for the...Ch. 13.3 - Evaluating Derivatives Find the following for the...Ch. 13.3 - Evaluating Derivatives Find the following for the...Ch. 13.3 - Evaluating Derivatives Find the following for the...Ch. 13.3 - Tangent Lines (a) If f(x) = x3 2x + 4, find f(a)....Ch. 13.3 - Tangent Lines (a) If g(x) = 1/(2x 1), find g(a)....Ch. 13.3 - Which Derivative Does the Limit Represent? The...Ch. 13.3 - Which Derivative Does the Limit Represent? The...Ch. 13.3 - Which Derivative Does the Limit Represent? The...Ch. 13.3 - Which Derivative Does the Limit Represent? The...Ch. 13.3 - Velocity of a Ball If a ball is thrown straight up...Ch. 13.3 - Velocity on the Moon If an arrow is shot upward on...Ch. 13.3 - Velocity of a Particle The displacement s (in...Ch. 13.3 - Inflating a Balloon A spherical balloon is being...Ch. 13.3 - Temperature Change A roast turkey is taken from an...Ch. 13.3 - Heart Rate A cardiac monitor is used to measure...Ch. 13.3 - Water Flow A tank holds 1000 gal of water, which...Ch. 13.3 - World Population Growth The table gives...Ch. 13.3 - DISCUSS: Estimating Derivatives from a Graph For...Ch. 13.3 - DISCUSS: Estimating Velocities from a Graph The...Ch. 13.4 - Let f be a function defined on some interval (a,...Ch. 13.4 - A sequence a1, a2, a3, has the limit L if the nth...Ch. 13.4 - Limits from a Graph (a) Use the graph of f to find...Ch. 13.4 - Limits from a Graph (a) Use the graph of f to find...Ch. 13.4 - Limits at Infinity Find the limit. 5. limx6xCh. 13.4 - Limits at Infinity Find the limit. 6. limx3x4Ch. 13.4 - Limits at Infinity Find the limit. 7. limx2x+15x1Ch. 13.4 - Limits at Infinity Find the limit. 8. limx23x4x+5Ch. 13.4 - Limits at Infinity Find the limit. 9....Ch. 13.4 - Limits at Infinity Find the limit. 10....Ch. 13.4 - Limits at Infinity Find the limit. 11....Ch. 13.4 - Limits at Infinity Find the limit. 12....Ch. 13.4 - Limits at Infinity Find the limit. 13....Ch. 13.4 - Limits at Infinity Find the limit. 14....Ch. 13.4 - Limits at Infinity Find the limit. 15....Ch. 13.4 - Limits at Infinity Find the limit. 16....Ch. 13.4 - Limits at Infinity Find the limit. 17. limxcosxCh. 13.4 - Limits at Infinity Find the limit. 18. limxsin2xCh. 13.4 - Estimating Limits Numerically and Graphically Use...Ch. 13.4 - Estimating Limits Numerically and Graphically Use...Ch. 13.4 - Estimating Limits Numerically and Graphically Use...Ch. 13.4 - Estimating Limits Numerically and Graphically Use...Ch. 13.4 - Limits of Sequences If the sequence with the given...Ch. 13.4 - Limits of Sequences If the sequence with the given...Ch. 13.4 - Limits of Sequences If the sequence with the given...Ch. 13.4 - Limits of Sequences If the sequence with the given...Ch. 13.4 - Limits of Sequences If the sequence with the given...Ch. 13.4 - Limits of Sequences If the sequence with the given...Ch. 13.4 - Limits of Sequences If the sequence with the given...Ch. 13.4 - Limits of Sequences If the sequence with the given...Ch. 13.4 - Limits of Sequences If the sequence with the given...Ch. 13.4 - Limits of Sequences If the sequence with the given...Ch. 13.4 - Limits of Sequences If the sequence with the given...Ch. 13.4 - Limits of Sequences If the sequence with the given...Ch. 13.4 - A Function from a Description Find a formula from...Ch. 13.4 - A Function from a Description Find a formula from...Ch. 13.4 - Asymptote Behavior How close to 3 do we have to...Ch. 13.4 - Equivalent Limits Show that...Ch. 13.4 - Salt Concentration (a) A tank contains 5000 L of...Ch. 13.4 - Velocity of a Raindrop The downward velocity of a...Ch. 13.4 - DISCUSS: The Limit of a Recursive Sequence (a) A...Ch. 13.5 - The graph of a function f is shown below. 1. To...Ch. 13.5 - Let Rn be the approximation obtained by using n...Ch. 13.5 - Estimating an Area Using Rectangles (a) By reading...Ch. 13.5 - Estimating an Area Using Rectangles (a) Use six...Ch. 13.5 - f(x)=12x+2Ch. 13.5 - Estimating Areas Using Rectangles Approximate the...Ch. 13.5 - Estimating Areas Using Rectangles Approximate the...Ch. 13.5 - Estimating Areas Using Rectangles Approximate the...Ch. 13.5 - Estimating Areas Using Rectangles In these...Ch. 13.5 - Estimating Areas Using Rectangles In these...Ch. 13.5 - Estimating Areas Using Rectangles In these...Ch. 13.5 - Estimating Areas Using Rectangles In these...Ch. 13.5 - Finding the Area Under A Curve Use the definition...Ch. 13.5 - Finding the Area Under A Curve Use the definition...Ch. 13.5 - Finding the Area Under a Curve Find the area of...Ch. 13.5 - Finding the Area Under a Curve Find the area of...Ch. 13.5 - Finding the Area Under a Curve Find the area of...Ch. 13.5 - Finding the Area Under a Curve Find the area of...Ch. 13.5 - Finding the Area Under a Curve Find the area of...Ch. 13.5 - Finding the Area Under a Curve Find the area of...Ch. 13.5 - DISCUSS: Approximating Area with a Calculator When...Ch. 13.5 - WRITE: Regions with Straight Versus Curved...Ch. 13 - (a) Explain what is meant by limxa f(x) = L. (b)...Ch. 13 - To evaluate the limit of a function, we often need...Ch. 13 - (a) Explain what it means to...Ch. 13 - (a) Define the derivative f(a) of a function f at...Ch. 13 - (a) Give two different interpretations of the...Ch. 13 - (a) Explain what is meant by limx f(x) = L. Draw...Ch. 13 - (a) If a1, a2, a3, is a sequence, what is meant...Ch. 13 - (a) Suppose S is the region under the graph of the...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Limits from a Graph The graph of f is shown in the...Ch. 13 - One-Sided Limits Let f(x)={2ifx1x2if1x2x+2ifx2...Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Derivative of a Function Find the derivative of...Ch. 13 - Derivative of a Function Find the derivative of...Ch. 13 - Derivative of a Function Find the derivative of...Ch. 13 - Derivative of a Function Find the derivative of...Ch. 13 - Evaluating Derivatives (a) Find f(a). (b) Find...Ch. 13 - Evaluating Derivatives (a) Find f(a). (b) Find...Ch. 13 - Evaluating Derivatives (a) Find f(a). (b) Find...Ch. 13 - Evaluating Derivatives (a) Find f(a). (b) Find...Ch. 13 - Equation of a Tangent Line Find an equation of the...Ch. 13 - Equation of a Tangent Line Find an equation of the...Ch. 13 - Equation of a Tangent Line Find an equation of the...Ch. 13 - Equation of a Tangent Line Find an equation of the...Ch. 13 - Equation of a Tangent Line Find an equation of the...Ch. 13 - Equation of a Tangent Line Find an equation of the...Ch. 13 - Velocity of a Dropped Stone A stone is dropped...Ch. 13 - Instantaneous Rate of Change If a gas is confined...Ch. 13 - Limit of a Sequence If the sequence is convergent,...Ch. 13 - Limit of a Sequence If the sequence is convergent,...Ch. 13 - Limit of a Sequence If the sequence is convergent,...Ch. 13 - Limit of a Sequence If the sequence is convergent,...Ch. 13 - Limit of a Sequence If the sequence is convergent,...Ch. 13 - Limit of a Sequence If the sequence is convergent,...Ch. 13 - Estimating Areas Using Rectangles Approximate the...Ch. 13 - Estimating Areas Using Rectangles Approximate the...Ch. 13 - Area Under a Curve Use the limit definition of...Ch. 13 - Area Under a Curve Use the limit definition of...Ch. 13 - Area Under a Curve Use the limit definition of...Ch. 13 - Area Under a Curve Use the limit definition of...Ch. 13 - (a) Use a table of values to estimate the...Ch. 13 - For the piecewise-defined function f whose graph...Ch. 13 - Evaluate the limit if it exists. (a) limx2x2+2x8x2...Ch. 13 - Let f(x) = x2 2x. Find: (a) f(x) (b) f(1), f(1),...Ch. 13 - Find the equation of the line tangent to the graph...Ch. 13 - Find the limit of the sequence. (a) an=nn2+4 (b)...Ch. 13 - The region sketched in the figure in the margin...Ch. 13 - Work Done by a Winch A motorized winch is being...Ch. 13 - Work Done by a Spring Hookes law states that when...Ch. 13 - Force of Water As any diver knows, an object...Ch. 13 - Distance Traveled by a Car Since distance = speed ...Ch. 13 - Heating Capacity If the outdoor temperature...

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