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Chapter 1: Q. 22 (page 135)

Use a geometric argument and the Squeeze Theorem for limits to argue that lim胃鈫�0鈭�鈥�sin鈦�胃=0

for sufficiently small negative angles 胃.

Short Answer

Expert verified

The given statement is proved.

Step by step solution

01

Step 1. Given information.

We have to use geometric argument and the Squeeze Theorem for limits to arguelim胃鈫�0鈭�鈥�sin鈦�胃=0

02

Step 2. Prove the given statement 

Look at the picture below:

Using Squeeze Theorem to calculate limits of sin胃at x = 0. take angle measured in radians 鈭�蟺4<胃<0

According to the figure, we clearly have 0<sin胃<胃. Since lim胃鈫�0鈭�鈥�0=0lim胃鈫�0鈭�鈥�胃=0,by Squeeze Theorem we must also have lim胃鈫�0鈭�鈥�sin鈦�胃=0

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Most popular questions from this chapter

Write delta-epsilon proofs for each of the limit statements limx鈫�cfx=Lin Exercises 47-60.

limx鈫�12x+4=6.

Use algebra to find the largest possible value of 未 or smallest possible value of N that makes each implication true. Then verify and support your answers with labeled graphs.
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Use algebra to find the largest possible value of 未 or smallest possible value of N that makes each implication true. Then verify and support your answers with labeled graphs.

Ifx>N, then1x2鈭�0<0.001

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For each limit statement , use algebra to find 未 > 0 in terms of 蔚> 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < 蔚.

limx鈫�3(x+5)=8
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