jee-main 2022 Q71

jee-main · India · session2_26jul_shift1 Differentiating Transcendental Functions Determine parameters from function or curve conditions

If the function $f ( x ) = \left\{ \begin{array} { l l } \frac { \log _ { e } \left( 1 - x + x ^ { 2 } \right) + \log _ { e } \left( 1 + x + x ^ { 2 } \right) } { \sec x - \cos x } , & x \in \left( \frac { - \pi } { 2 } , \frac { \pi } { 2 } \right) - \{ 0 \} \\ k & , x = 0 \end{array} \right.$ is continuous at $x = 0$, then $k$ is equal to:
(1) 1
(2) $- 1$
(3) $e$
(4) 0

If the function $f ( x ) = \left\{ \begin{array} { l l } \frac { \log _ { e } \left( 1 - x + x ^ { 2 } \right) + \log _ { e } \left( 1 + x + x ^ { 2 } \right) } { \sec x - \cos x } , & x \in \left( \frac { - \pi } { 2 } , \frac { \pi } { 2 } \right) - \{ 0 \} \\ k & , x = 0 \end{array} \right.$ is continuous at $x = 0$, then $k$ is equal to:\\
(1) 1\\
(2) $- 1$\\
(3) $e$\\
(4) 0

Paper Questions

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