Explanation Given: lim x → 0 x 4 cos ( 2 x ) Formula used: − 1 ≤ cos x ≤ 1 If f ( x ) ≤ z ( x ) ≤ g ( x ) , then lim x → a f ( x ) ≤ lim x → a z ( x ) ≤ lim x → a g ( x ) . Calculation: − 1 ≤ cos ( 2 x ) ≤ 1 Multiply the above inequality by x 4 . − x 4 ≤ x 4 cos ( 2 x ) ≤ x 4 Take limit tending to 0 in the above inequality

15th Edition

ISBN: 9781305420878

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 2.4, Problem 31E

To determine

The limit of the given function.

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Chapter 2.4, Problem 30E

Chapter 2.4, Problem 32E

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Chapter 2 Solutions

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The limit of the given function.

Solution Summary: The author calculates the limit of the given function by multiplying the above inequality by x4.

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Chapter 2 Solutions