Explanation Given information: The given limit is lim h → 0 3 ( 2 + h ) 2 − ( 2 + h ) − 10 h . Calculation: The given limit can be written as, lim h → 0 3 ( 2 + h ) 2 − ( 2 + h ) − 10 h = lim h → 0 [ 3 ( 2 + h ) 2 − ( 2 + h ) − 10 ] − [ 0 ] h = lim h → 0 [ 3 ( 2 + h ) 2 − ( 2 + h ) − 10 ] − [ 3 ( 2 ) 2 − 2 − 10 ] h Use the definition of derivative of any function f . f ′ ( x ) = lim h → 0 f ( x + h ) − f ( x ) h Substitute 2 for x in the above definition of derivative. f ′ ( 2 ) = lim h → 0 f ( 2 + h ) − f ( 2 ) h Compare the given limit and the limit in the derivative f ′ ( 2 ) . This means that f ( 2 + h ) = 3 ( 2 + h ) 2 − ( 2 + h ) − 10 and f ( 2 ) = 3 ( 2 ) 2 − 2 − 10

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 39E

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 38E

Chapter 3.1, Problem 40E

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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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AUTO TRANSMISSIONS .AND FUEL ECONOMY In trying to...Ch. 3.5 - Prob. 32E Ch. 3.5 - Prob. 33E Ch. 3.5 - Prob. 34E Ch. 3.5 - Prob. 35E Ch. 3.5 - Prob. 36E Ch. 3.5 - Prob. 37E Ch. 3.5 - Prob. 38E Ch. 3.5 - Prob. 39E Ch. 3.5 - Prob. 40E Ch. 3.5 - Prob. 41E Ch. 3.5 - Prob. 42E Ch. 3.5 - Prob. 43E Ch. 3.5 - Prob. 44E Ch. 3.5 - Prob. 45E Ch. 3.5 - Prob. 46E Ch. 3.5 - Prob. 47E Ch. 3.5 - Prob. 48E Ch. 3.5 - Prob. 49E Ch. 3.5 - Prob. 50E Ch. 3.5 - Prob. 1TE Ch. 3.5 - Prob. 2TE Ch. 3.5 - Prob. 3TE Ch. 3.5 - Prob. 4TE Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - Prob. 6TE Ch. 3.5 - Prob. 7TE Ch. 3.5 - Prob. 8TE Ch. 3.6 - Prob. 1CQ Ch. 3.6 - Prob. 2CQ Ch. 3.6 - Prob. 3CQ Ch. 3.6 - Prob. 4CQ Ch. 3.6 - Prob. 1E Ch. 3.6 - Prob. 2E Ch. 3.6 - Prob. 3E Ch. 3.6 - Prob. 4E Ch. 3.6 - Prob. 5E Ch. 3.6 - Prob. 6E Ch. 3.6 - Prob. 7E Ch. 3.6 - Prob. 8E Ch. 3.6 - Prob. 9E Ch. 3.6 - Prob. 10E Ch. 3.6 - Prob. 11E Ch. 3.6 - Prob. 12E Ch. 3.6 - Prob. 13E Ch. 3.6 - Prob. 14E Ch. 3.6 - Prob. 15E Ch. 3.6 - 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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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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