Explanation Given information: The given limit is lim h → 0 ( 1 + h ) 3 − 1 h . Calculation: The given limit can be written as, lim h → 0 ( 1 + h ) 3 − 1 h = lim h → 0 ( 1 + h ) 3 − ( 1 ) 3 h Use the definition of derivative of any function f . f ′ ( x ) = lim h → 0 f ( x + h ) − f ( x ) h Substitute 1 for x in the above derivative. f ′ ( 1 ) = lim h → 0 f ( 1 + h ) − f ( 1 ) h Compare the given limit and the limit in the derivative f ′ ( 1 ) . This means that f ( 1 + h ) = ( 1 + h ) 3 and f ( 1 ) = ( 1 ) 3 . The required function has cubic power

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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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 3.1, Problem 37E

To determine

The value of the given limit with the help of derivative of a suitable function at an appropriate point.

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Chapter 3.1, Problem 36E

Chapter 3.1, Problem 38E

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(11 points) Use the given graph of the function g to find the following limits: 1. lim g(x): = x→2 2. lim g(x) = x→2+ 3. lim g(x) = x→2 4. lim g(x) = x→0 5. g(2) = 110 help (limits)

Use a graph to explain the meaning

EXPLAIN: Exercise 4.1 1. Explain the difference between the one-sided limit from the right and the one-sided limit from the left. 2. When do you say that the limit of the function exists? 5

Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The value of the given limit with the help of derivative of a suitable function at an appropriate point.

Solution Summary: The author calculates the value of the given limit with the help of derivative of a suitable function at an appropriate point.

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The value of the given limit with the help of derivative of a suitable function at an appropriate point.

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Chapter 3 Solutions