Question

If f(1) = 1, f ′(1) = 2 then $f(x) = \left\{ \begin{matrix} \tan^{- 1}x & , & |x| \leq 1 \\ \frac{1}{2}(|x| - 1) & , & |x| > 1 \end{matrix} \right.$ R - { 0} =

• A. 2
• B. 1
• C. 3
• D. 4

Answer 1

Answer: (A)

2

Answer 2

$\lim _ { x \rightarrow 1 }$ ; $\frac { 0 } { 0 }$ form

⇒ $\lim _ { x \rightarrow 1 }$ = $\frac { \mathrm { f } ^ { \prime } ( 1 ) } { \sqrt { \mathrm { f } ( 1 ) } }$ . $\sqrt { 1 }$ = 2