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Chapter 10: Q. 54 (page 777)

$\lim_{x \to 0} (\frac{e^{x} - 1}{x})$

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information

$\lim_{x \to 0} (\frac{e^{x} - 1}{x})$

02

Step 2. Plug in the values

Applying L'Hopital's rule,

\lim_{x \to 0} (\frac{e^{x} - 1}{x}) = \lim_{x \to 0} (\frac{e^{x}}{1})

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

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

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Most popular questions from this chapter

What is the definition of the triple scalar product for vectors u, v and w in $ℝ^{3}$ ?

Find $u + v$ and $u - v$ . Also, sketch $u, v, u + v$ and $u - v$ .

role="math" localid="1649572653771" $u = (2, - 6), v = (6, 2)$ ,

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