If the function f(x) = begincases (1+|cos x|)(λ)/(|cos x|), & 0 < x < (π)/2 \ μ, & x = (π)/2 \ dfraccot 6xe^cot 4x, & (π)/2 < x < π endcases is continuous at x = (π)/2, then 9λ + 6log_e μ + μ^6 - e^6λ is equal to

If the function f(x) = begincases (1+|cos x|)(λ)/(|cos x|),… — JEE Main 2023 Mathematics PYQ

JEE Main 2023 · 25 Jan · Shift 2

If the function

f(x) = \begin{cases} (1+|\cos x|)\dfrac{\lambda}{|\cos x|}, & 0 < x < \dfrac{\pi}{2} \\ \mu, & x = \dfrac{\pi}{2} \\ \dfrac{\cot 6x}{e^{\cot 4x}}, & \dfrac{\pi}{2} < x < \pi \end{cases}

is continuous at

x = \dfrac{\pi}{2}

, then

9\lambda + 6\log_e \mu + \mu^6 - e^{6\lambda}

is equal to

Show answer

Correct option: C

[JEE Main 2023 · 25 Jan · Shift 2]

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