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Chapter 1: Q. 93 (page 151)

Prove the k=1 case of the second part of Theorem 1.31(b): that limx鈫�鈭�e-x=0.

Short Answer

Expert verified

It is proved for theorem1.31bthatlimx鈫�鈭�e-x=0.

Step by step solution

01

Step 1. Given Information 

We are given,

limx鈫�鈭�e-x=0

02

Step 2. Proving the statement 

The limit is given by,

limx鈫�鈭�e-x=limx鈫�鈭�1ex=1e鈭�=1鈭�=0

Hence Proved.

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Most popular questions from this chapter

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�21x=12;youmayassume未鈮�1

Each function in Exercises 9鈥�12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.

limx鈫�0-f(x)=-1,limx鈫�0+f(x)=1,f(0)=0.

For each limit in Exercises 33鈥�38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

limx鈫�-16.

What are punctured intervals, and why do we need to use them when discussing limits?

limx鈫�+22x-4
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