First slide

Introduction to limits

Question

The value of $lim_{x \to \infty} x^{1 / x}$ equals

Moderate

A

0
B

1
C

$e$
D

$e^{- 1}$

Solution

Let $A = lim_{x \to \infty} x^{1 / x}$ Then,
$\begin{array}{l} \log A = lim_{x \to \infty} \frac{1}{x} \log x = 0 [∵ lim_{x \to \infty} \frac{\log x}{x^{m}} = 0, for all m > 0] \\ \Rightarrow A = e^{0} = 1 . \end{array}$

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