First slide

Introduction to limits

Question

The value of $\underset{x \to 0}{L t} \frac{{(1 + x)}^{\frac{1}{x}} - e}{x}$

Moderate

A

1
B

$\frac{e}{2}$
C

$- \frac{e}{2}$
D

$\frac{2}{e}$

Solution

$\begin{matrix} \underset{x \to 0}{L t} \frac{{(1 + x)}^{1 / x} - e}{x} = \lim_{x \to 0} \frac{e (1 - \frac{x}{2} + \frac{11}{24} x^{2} - . . . .) - e}{x} \end{matrix}$
= $\lim_{x \to 0} \frac{x (\frac{- e}{2} + \frac{11 e}{24} x - . . . . . .)}{x}$
= $\frac{- e}{2}$

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