Question

$\lim_{x \rightarrow 0}x^{x} =$

• A. 0
• B. 1
• C. e
• D. None of these

Answer 1

Answer: (B)

1

Answer 2

Let $y = x^{x} \Rightarrow \log y = x\log x$

$\therefore\lim_{y \rightarrow 0}\log y = \lim_{x \rightarrow 0}x\log x = 0 = \log 1 \Rightarrow \lim_{x \rightarrow 0}x^{x} = 1$