Explanation Given: The limit derivative of the function is given as: lim t → 1 t + 1 − 2 t − 1 The derivative of the function at the point P ( a , f ( a ) ) between the number x and a is represented as: f ′ ( a ) = lim x → a f ( x ) − f ( a ) x − a at x = a , (1) Calculation: Section1: To find t he function in the given limit derivative. Now, compare the given limit derivative of the function with equation (1). lim x → a f ( x ) − f ( a ) x − a = lim t → 1 t + 1 − 2 t − 1 <

7th Edition

ISBN: 9780357293270

Author: Stewart

Publisher: CENGAGE L

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 13.3, Problem 35E

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To evaluate: The function f and the number a in the given limit derivative of a function.

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Chapter 13.3, Problem 34E

Chapter 13.3, Problem 36E

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Chapter 13 Solutions

PRECALCULUS LL + WEBASSIGN/COREQUISITE

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 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

Ch. 13.1 - Prob. 11E Ch. 13.1 - Prob. 12E Ch. 13.1 - Prob. 13E Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Prob. 15E Ch. 13.1 - Prob. 16E Ch. 13.1 - Prob. 17E 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 - Prob. 21E Ch. 13.1 - Prob. 22E Ch. 13.1 - Prob. 23E Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Prob. 25E Ch. 13.1 - Prob. 26E Ch. 13.1 - Prob. 27E Ch. 13.1 - Prob. 28E Ch. 13.1 - Prob. 29E Ch. 13.1 - One-Sided Limits Graph the piecewise-defined...Ch. 13.1 - Prob. 31E Ch. 13.1 - Prob. 32E Ch. 13.1 - Prob. 33E 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 - Prob. 4E Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Prob. 6E Ch. 13.2 - Prob. 7E Ch. 13.2 - Prob. 8E Ch. 13.2 - Prob. 9E Ch. 13.2 - Prob. 10E Ch. 13.2 - Prob. 11E Ch. 13.2 - Prob. 12E Ch. 13.2 - Prob. 13E Ch. 13.2 - Prob. 14E Ch. 13.2 - Prob. 15E Ch. 13.2 - Prob. 16E Ch. 13.2 - Prob. 17E Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Prob. 19E Ch. 13.2 - Prob. 20E Ch. 13.2 - Prob. 21E Ch. 13.2 - Prob. 22E Ch. 13.2 - Prob. 23E Ch. 13.2 - Prob. 24E Ch. 13.2 - Prob. 25E Ch. 13.2 - Prob. 26E Ch. 13.2 - Prob. 27E Ch. 13.2 - Prob. 28E Ch. 13.2 - Prob. 29E Ch. 13.2 - Prob. 30E Ch. 13.2 - Prob. 31E Ch. 13.2 - Prob. 32E Ch. 13.2 - Prob. 33E Ch. 13.2 - Prob. 34E Ch. 13.2 - Prob. 35E Ch. 13.2 - Prob. 36E Ch. 13.2 - Prob. 37E Ch. 13.2 - Prob. 38E Ch. 13.2 - Prob. 39E Ch. 13.2 - Prob. 40E 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 - Prob. 44E Ch. 13.2 - Finding Limits Numerically and Graphically (a)...Ch. 13.2 - Prob. 46E Ch. 13.2 - Prob. 47E Ch. 13.2 - Prob. 48E 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 - Prob. 2E Ch. 13.3 - Prob. 3E Ch. 13.3 - Prob. 4E Ch. 13.3 - Prob. 5E Ch. 13.3 - Prob. 6E Ch. 13.3 - Prob. 7E Ch. 13.3 - Prob. 8E Ch. 13.3 - Prob. 9E Ch. 13.3 - Prob. 10E Ch. 13.3 - Prob. 11E Ch. 13.3 - Prob. 12E Ch. 13.3 - Equation of a Tangent Line Find an equation of the...Ch. 13.3 - Prob. 14E Ch. 13.3 - Prob. 15E Ch. 13.3 - Prob. 16E Ch. 13.3 - Prob. 17E Ch. 13.3 - Prob. 18E Ch. 13.3 - Prob. 19E Ch. 13.3 - Prob. 20E Ch. 13.3 - Prob. 21E Ch. 13.3 - Prob. 22E Ch. 13.3 - Prob. 23E Ch. 13.3 - Prob. 24E Ch. 13.3 - Prob. 25E Ch. 13.3 - Prob. 26E Ch. 13.3 - Prob. 27E Ch. 13.3 - Prob. 28E Ch. 13.3 - Prob. 29E Ch. 13.3 - Prob. 30E Ch. 13.3 - Prob. 31E Ch. 13.3 - Tangent Lines (a) If g(x) = 1/(2x 1), find g(a)....Ch. 13.3 - Prob. 33E Ch. 13.3 - Prob. 34E Ch. 13.3 - Prob. 35E Ch. 13.3 - Prob. 36E 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 - Prob. 39E 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 - Prob. 43E Ch. 13.3 - World Population Growth The table gives...Ch. 13.3 - Prob. 45E Ch. 13.3 - Prob. 46E Ch. 13.4 - Let f be a function defined on some interval (a,...Ch. 13.4 - Prob. 2E Ch. 13.4 - Limits from a Graph (a) Use the graph of f to find...Ch. 13.4 - Prob. 4E Ch. 13.4 - Prob. 5E Ch. 13.4 - Prob. 6E Ch. 13.4 - Prob. 7E Ch. 13.4 - Prob. 8E Ch. 13.4 - Prob. 9E Ch. 13.4 - Prob. 10E Ch. 13.4 - Prob. 11E Ch. 13.4 - Prob. 12E Ch. 13.4 - Prob. 13E Ch. 13.4 - Prob. 14E Ch. 13.4 - Prob. 15E Ch. 13.4 - Prob. 16E Ch. 13.4 - Limits at Infinity Find the limit. 17. limxcosx Ch. 13.4 - Prob. 18E Ch. 13.4 - Prob. 19E Ch. 13.4 - Prob. 20E Ch. 13.4 - Estimating Limits Numerically and Graphically Use...Ch. 13.4 - Prob. 22E Ch. 13.4 - Prob. 23E Ch. 13.4 - Prob. 24E Ch. 13.4 - Prob. 25E Ch. 13.4 - Prob. 26E Ch. 13.4 - Prob. 27E Ch. 13.4 - Prob. 28E Ch. 13.4 - Prob. 29E Ch. 13.4 - Prob. 30E Ch. 13.4 - Prob. 31E Ch. 13.4 - Prob. 32E Ch. 13.4 - Prob. 33E Ch. 13.4 - Prob. 34E Ch. 13.4 - Prob. 35E Ch. 13.4 - Prob. 36E Ch. 13.4 - Prob. 37E Ch. 13.4 - Prob. 38E 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 - Prob. 2E Ch. 13.5 - Estimating an Area Using Rectangles (a) By reading...Ch. 13.5 - Prob. 4E Ch. 13.5 - Prob. 5E Ch. 13.5 - Prob. 6E Ch. 13.5 - Prob. 7E Ch. 13.5 - Prob. 8E Ch. 13.5 - Prob. 9E Ch. 13.5 - Estimating Areas Using Rectangles In these...Ch. 13.5 - Prob. 11E Ch. 13.5 - Prob. 12E Ch. 13.5 - Prob. 13E Ch. 13.5 - Prob. 14E Ch. 13.5 - Prob. 15E Ch. 13.5 - Prob. 16E Ch. 13.5 - Prob. 17E Ch. 13.5 - Prob. 18E Ch. 13.5 - Prob. 19E Ch. 13.5 - Prob. 20E Ch. 13.5 - Prob. 21E Ch. 13.5 - Prob. 22E 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 - Prob. 13RE Ch. 13 - Prob. 14RE Ch. 13 - Prob. 15RE Ch. 13 - Prob. 16RE Ch. 13 - Prob. 17RE Ch. 13 - Prob. 18RE Ch. 13 - Prob. 19RE Ch. 13 - Prob. 20RE Ch. 13 - Prob. 21RE Ch. 13 - Derivative of a Function Find the derivative of...Ch. 13 - Prob. 23RE Ch. 13 - Prob. 24RE Ch. 13 - Prob. 25RE Ch. 13 - Prob. 26RE Ch. 13 - Prob. 27RE Ch. 13 - Prob. 28RE Ch. 13 - Prob. 29RE Ch. 13 - Prob. 30RE Ch. 13 - Prob. 31RE Ch. 13 - Prob. 32RE Ch. 13 - Prob. 33RE Ch. 13 - Prob. 34RE Ch. 13 - Prob. 35RE Ch. 13 - Prob. 36RE Ch. 13 - Prob. 37RE Ch. 13 - Prob. 38RE Ch. 13 - Prob. 39RE Ch. 13 - Prob. 40RE Ch. 13 - Prob. 41RE Ch. 13 - Prob. 42RE Ch. 13 - Prob. 43RE Ch. 13 - Prob. 44RE Ch. 13 - Prob. 45RE Ch. 13 - Prob. 46RE Ch. 13 - Prob. 47RE Ch. 13 - Prob. 48RE Ch. 13 - Prob. 1T Ch. 13 - For the piecewise-defined function f whose graph...Ch. 13 - Prob. 3T Ch. 13 - Prob. 4T Ch. 13 - Prob. 5T Ch. 13 - Prob. 6T Ch. 13 - Prob. 7T Ch. 13 - Work Done by a Winch A motorized winch is being...Ch. 13 - Prob. 2P Ch. 13 - Prob. 3P Ch. 13 - Prob. 4P Ch. 13 - Prob. 5P

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The function f and the number a in the given limit derivative of a function.

Solution Summary: The author evaluates the function f and the number a in the given limit derivative of a function.

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To evaluate: The function f and the number a in the given limit derivative of a function.

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Chapter 13 Solutions