The value of limx→∞ x1/x equals

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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