Question

Given a real valued function ‘f’ such that

f(x) = $\left\{ \begin{matrix} \frac{\tan^{2}\{ x\}}{x^{2} - \lbrack x\rbrack^{2}} & forx > 0 \\ 1 & forx = 0 \\ \sqrt{\{ x\}\cot\{ x\}} & forx < 0 \end{matrix} \right.\$ then the value of cot^–1$\left( \underset{x \rightarrow 0}{Lim}f(x) \right)^{2}$is –

• A. 0
• B. 1
• C. –1
• D. None

Answer 1

Answer: (D)

None

Answer 2

$\operatorname { Lim } _ { x \rightarrow 0 ^ { - } }$ f(x) = $\sqrt { \{ - \mathrm { h } \} \cot \{ - \mathrm { h } \} }$

= $\sqrt { ( 1 - \mathrm { h } ) \cot ( 1 - \mathrm { h } ) }$ = $\sqrt { \cot 1 }$

$\operatorname { Lim } _ { x \rightarrow 0 ^ { + } }$f(x) = = = 1

∴ f(x) does not exist.