Question

Let f(x) = x(–1)^[1/x], x ¹ 0, where [x] denotes the greatest integer less than or equal to x then, $\lim_{x \rightarrow 0}$f(x) =

• A. Doesn't exist
• B. 2
• C. 0
• D. –1

Answer 1

Answer: (C)

0

Answer 2

Q [1/x] = Integer

\ (–1)^[1/x] 1 or –1

$\lim_{x \rightarrow 0}$x (–1)^[1/x]

& \lim_{h \rightarrow 0}(h)(1or - 1) = 0 \\ & \lim_{h \rightarrow 0}( - h)(1or - 1) = 0 \end{aligned} \right\rbrack$$