Question

Let ƒ(x) = sgn (sgn (sgn x)). Then $\lim_{x \rightarrow 0}$ƒ(x) is –

• A. 1
• B. 2
• C. 0
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

By definition we have for x ≠ 0, sgn (sgn x)

= sgn $\left( \frac { x } { | x | } \right)$

= = = sgn x. Thus, sgn [sgn)

(sgn x) = sgn x = $\left\{ \begin{array} { r l } 1 & x > 0 \\ 0 & x = 0 \\ - 1 & x < 0 \end{array} \right.$

Therefore, $\lim _ { x \rightarrow 0 + }$ ƒ(x) = 1 but $\lim _ { x \rightarrow 0 - }$ ƒ(x) = –1.