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Chapter 10: Q. 54 (page 777)

$\lim_{x 鈫� 0} (\frac{e^{x} - 1}{x})$

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information

$\lim_{x 鈫� 0} (\frac{e^{x} - 1}{x})$

02

Step 2. Plug in the values

Applying L'Hopital's rule,

\lim_{x 鈫� 0} (\frac{e^{x} - 1}{x}) = \lim_{x 鈫� 鈥� 0} (\frac{e^{x}}{1})

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

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

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Most popular questions from this chapter

Find $u + v a n d u - v$ also sketch $u, v, u + v, u - v$

role="math" localid="1649603034674" $u = (1, - 4, 6) a n d v = (2, - 4, 7)$

In Exercises 24-27, find ${comp}_{u} v, {proj}_{u} v$ and the component of v orthogonal tou.

$u = <2, 0, - 5>, v = <- 3, 7, - 1>$

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Find $\overset{鈫�}{P Q}$ .

$P = (3, 6), Q = (鈭� 3, 鈭� 2)$

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$\lim_{h 鈫� 0} \frac{\frac{1}{1 + h} - 1}{h}$ .

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