CALCULUS
CALCULUS
11th Edition
ISBN: 9780357092477
Author: Larson
Publisher: Cengage
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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 1.3, Problem 124E

Approximation

(a) Find lim x → 0 1 − cos   x x 2 .

(b) Use your answer to part (a) to device the approximation cos   x ≈ 1 − 1 2 x 2 for x near 0.

(c) Use your answer to part (b) to approximate cos(0.1).

(d) Use a calculator to approximate cos(0.1) to four decimal places. Compare the result with part (c).

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Chapter 1 Solutions

CALCULUS

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Use the graph of f to identify...Ch. 1.2 - Prob. 73ECh. 1.2 - Prob. 74ECh. 1.2 - Prob. 75ECh. 1.2 - Prob. 76ECh. 1.2 - Prob. 77ECh. 1.2 - Prob. 78ECh. 1.2 - Evaluating Limits Use a graphing utility to...Ch. 1.2 - Prob. 80ECh. 1.2 - Proof Prove that if the limit of f(x) as x...Ch. 1.2 - Prob. 82ECh. 1.2 - Prob. 83ECh. 1.2 - Prob. 84ECh. 1.2 - Inscribe a rectangle of base b and height h in a...Ch. 1.2 - Prob. 86ECh. 1.2 - Estimating a Limit Numerically In Exercises 5-10,...Ch. 1.2 - Estimating a Limit Numerically In Exercises 5-10,...Ch. 1.3 - CONCEPT CHECK Polynomial Function Describe how to...Ch. 1.3 - Prob. 2ECh. 1.3 - Squeeze Theorem In your own words, explain the...Ch. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - Finding a Limit In Exercises 5-22. find the limit....Ch. 1.3 - Prob. 7ECh. 1.3 - Finding a Limit In Exercises 5-22. find the limit....Ch. 1.3 - Prob. 9ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 11ECh. 1.3 - Prob. 10ECh. 1.3 - Prob. 15ECh. 1.3 - Finding a Limit In Exercises 5-22, find the limit....Ch. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Finding a Limit In Exercises 5-22, find the limit....Ch. 1.3 - Finding Limits In Exercises 23-26, Find the...Ch. 1.3 - Finding Limits In Exercises 23-26, Find the...Ch. 1.3 - Finding Limits In Exercises 23-26, Find the...Ch. 1.3 - Prob. 26ECh. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Prob. 28ECh. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Prob. 32ECh. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Prob. 34ECh. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Evaluating Limits In Exercises 37-40, use the...Ch. 1.3 - Evaluating Limits In Exercises 37-40, use the...Ch. 1.3 - Evaluating Limits In Exercises 37-40, use the...Ch. 1.3 - Finding a Limit In Exercises 41-46, write a...Ch. 1.3 - Finding a Limit In Exercises 41-46, write a...Ch. 1.3 - Finding a Limit In Exercises 41-46, write a...Ch. 1.3 - Finding a Limit In Exercises 41-46, write a...Ch. 1.3 - Finding a Limit In Exercises 41-46, write a...Ch. 1.3 - Finding a Limit In Exercises 41-46, write a...Ch. 1.3 - Prob. 47ECh. 1.3 - Prob. 48ECh. 1.3 - Finding a Limit In Exercises 4762, find the limit....Ch. 1.3 - Finding a Limit In Exercises 4762, find the limit....Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Prob. 55ECh. 1.3 - Prob. 56ECh. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Prob. 58ECh. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Prob. 61ECh. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Prob. 71ECh. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Prob. 73ECh. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Prob. 75ECh. 1.3 - Prob. 76ECh. 1.3 - Prob. 77ECh. 1.3 - Prob. 78ECh. 1.3 - Prob. 79ECh. 1.3 - Prob. 80ECh. 1.3 - Prob. 81ECh. 1.3 - Prob. 82ECh. 1.3 - Prob. 83ECh. 1.3 - Finding a Limit In Exercises 83-90, find...Ch. 1.3 - Prob. 85ECh. 1.3 - Finding a Limit In Exercises 83-90, find...Ch. 1.3 - Prob. 87ECh. 1.3 - Prob. 88ECh. 1.3 - Prob. 89ECh. 1.3 - Prob. 90ECh. 1.3 - Using the Squeeze Theorem In Exercises 91 and 92,...Ch. 1.3 - Using the Squeeze Theorem In Exercises 91 and 92,...Ch. 1.3 - Using the Squeeze Theorem In Exercises 93-96, use...Ch. 1.3 - Using the Squeeze Theorem In Exercises 93-96, use...Ch. 1.3 - Prob. 95ECh. 1.3 - Prob. 96ECh. 1.3 - Functions That Agree at All but One Point (a) In...Ch. 1.3 - Prob. 98ECh. 1.3 - Prob. 99ECh. 1.3 - HOW DO YOU SEE IT? 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