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7th Edition

James Stewart + 2 others

Publisher: Brooks Cole

ISBN: 9781305071759

Chapter 13.4, Problem 32E

Textbook Problem

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

**32.**

Precalculus: Mathematics for Calculus (Standalone Book)

Ch. 13.1 - When we write limxaf(x)=L then, roughly speaking,...Ch. 13.1 - We write limxaf(x)=L and say that the ______ of...Ch. 13.1 - Estimating Limits Numerically and Graphically...Ch. 13.1 - Estimating Limits Numerically and Graphically...Ch. 13.1 - Estimating Limits Numerically Complete the table...Ch. 13.1 - Estimating Limits Numerically Complete the table...Ch. 13.1 - Estimating Limits Numerically Complete the table...Ch. 13.1 - Estimating Limits Numerically Complete the table...Ch. 13.1 - Estimating Limits Numerically Complete the table...Ch. 13.1 - Estimating Limits Numerically Complete the table...

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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