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Chapter 1: Q. 10 (page 153)

Limits of basic functions: Fill in the blanks to complete the limit rules that follow. You may assume that $k$ is positive
$\lim_{x 鈫� 鈭�} e^{- k x} = ?$

Short Answer

Expert verified

The value of the limit $\lim_{x 鈫� 鈭�} e^{- k x} = 0 .$

Step by step solution

01

Step 1. Given Information.

The given limit function is $\lim_{x 鈫� 鈭�} e^{- k x} .$

02

Step 2. Value of the limit.

We know,

If $k > 0,$

Then,

$\lim_{x 鈫� 鈭�} e^{- k x} = 0$

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Most popular questions from this chapter

$\lim_{x 鈫� 0} (\frac{e^{x} - 1}{e^{2 x} + 2 e^{x} - 3})$

Write delta-epsilon proofs for each of the limit statements $\lim_{x 鈫� c} f (x) = L$ in Exercises $47 - 60$ .

$\lim_{x 鈫� 0} (3 x^{2} + 1) = 1$ .

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

$\lim_{x 鈫� - 1} x .$

Calculate each of the limits:

$\lim_{x 鈫� 3} \frac{\sqrt{x}}{\tan^{- 1} \sqrt{x}}$

Write delta-epsilon proofs for each of the limit statements $\lim_{x 鈫� c} f (x) = L$ in Exercises $47 - 60$ .

$\lim_{x 鈫� 3} (x^{2} - 6 x + 11) = 2$ .

See all solutions

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