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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
$\lim_{x \to \infty} e^{- k x} = ?$

Short Answer

Expert verified

The value of the limit $\lim_{x \to \infty} e^{- k x} = 0 .$

Step by step solution

01

Step 1. Given Information.

The given limit function is $\lim_{x \to \infty} e^{- k x} .$

02

Step 2. Value of the limit.

We know,

If $k > 0,$

Then,

$\lim_{x \to \infty} e^{- k x} = 0$

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For each limit statement , use algebra to find δ > 0 in terms of $ε$ > 0 so that if 0 < |x − c| < δ, then | f(x) − L| < $ε$ .

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