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Chapter 1: Q. 9 (page 153)

Limits of basic functions: Fill in the blanks to complete the limit rules that follow. You may assume that kis positive

limx鈫�鈭�ekx=?.

Short Answer

Expert verified

The value of the limit is鈭�.

Step by step solution

01

Step 1. Given Information.

The given limit function islimx鈫�鈭�ekx.

02

Step 2. Value of the limit.

We know,

Ifk>0,

Then,

limx鈫�鈭�ekx=鈭�

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Most popular questions from this chapter

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�-1x.

State what it means for a functionf to be continuous at a point x = c, in terms of the delta鈥揺psilon definition of limit.

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(x2-2x-3)=0;youmayassume未鈮�1

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

limx鈫�12x+4=6.

For each limit statement in Exercises 41-44, use algebra to find 未or Nin terms of 蔚or M, according to the appropriate formal limit definition.

limx鈫�1-11-x=鈭�, find未in terms ofM.
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