If the function … is continuous at …, then … is equal to

Limits Continuity and Differentiability

JEE Main 2023 · 25 Jan, Evening shift · Q4159

MathematicsMedium179×since 2002Q4159

If the function

f(x) = \left\{ {\matrix{ {(1 + |\cos x|)^{\lambda \over {|\cos x|}}} & , & {0 < x < {\pi \over 2}} \cr \mu & , & {x = {\pi \over 2}} \cr e^{{{\cot 6x} \over {{}\cot 4x}}} & , & {{\pi \over 2} < x < \pi } \cr } } \right.

is continuous at

x = {\pi \over 2}

, then

9\lambda + 6{\log _e}\mu + {\mu ^6} - {e^{6\lambda }}

is equal to

JEE Main 2023 · 25 Jan, Evening shift · Q4159

MathematicsMedium179×since 2002Q4159

If the function

f(x) = \left\{ {\matrix{ {(1 + |\cos x|)^{\lambda \over {|\cos x|}}} & , & {0 < x < {\pi \over 2}} \cr \mu & , & {x = {\pi \over 2}} \cr e^{{{\cot 6x} \over {{}\cot 4x}}} & , & {{\pi \over 2} < x < \pi } \cr } } \right.

is continuous at

x = {\pi \over 2}

, then

9\lambda + 6{\log _e}\mu + {\mu ^6} - {e^{6\lambda }}

is equal to