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Chapter 1: Q 80. (page 149)

Find the limit.
$\lim_{x 鈫� 鈭�} {(1 - \frac{5}{x})}^{x}$

Short Answer

Expert verified

Answer is $\frac{1}{e^{5}}$

Step by step solution

Step 1. Given information

Limit function is $\lim_{x 鈫� 鈭�} {(1 - \frac{5}{x})}^{x}$

Step 2. Explanation

Let $\frac{5}{x} = - h$

$\begin{array}{rcl} \lim_{x 鈫� 鈭�} {(1 - \frac{5}{x})}^{x} & = & \lim_{h 鈫� 0} {(1 + h)}^{\frac{- 5}{h}} \\ = & \lim_{h 鈫� 0} [\frac{1}{{(1 + h)}^{\frac{5}{h}}}] \\ = & \frac{1}{e^{5}} \end{array}$

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Most popular questions from this chapter

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

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$\lim_{x 鈫� - 1} x .$

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Find the limit.limx鈫�鈭�1-5xx

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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Find the limit.
$\lim_{x 鈫� 鈭�} {(1 - \frac{5}{x})}^{x}$