QJEEM19Ma431e: JEE Main 2019 Mathematics - Class 12 JEEM19Ma431e Solution: If the function ƒ defined on , by is continuous, then k is…

Question

Verified Solution • 2025–26 Session moderate

If the function ƒ defined on ,

\left( {{\pi \over 6},{\pi \over 3}} \right)

by

\sqrt 2

Accepted Answer

\mathop {\lim }\limits_{x \to {\pi \over 4}} {{\sqrt 2 \cos x - 1} \over {\cot x - 1}}

= f(

{{\pi \over 4}}

) = k

\mathop {\lim }\limits_{x \to {\pi \over 4}} {{\sqrt 2 \cos x - 1} \over {\cot x - 1}}

(

{0 \over 0}

form) = k

\Rightarrow

\mathop {\lim }\limits_{x \to {\pi \over 4}} {{ - \sqrt 2 \sin x} \over {-\cos e{c^2}x}}

(Using L Hospital Rule)

\Rightarrow

\mathop {\lim }\limits_{x \to {\pi \over 4}} \sqrt 2 {\sin ^3}x

= k

\Rightarrow

k =

\sqrt 2 {\left( {{1 \over {\sqrt 2 }}} \right)^3}

=

{1 \over 2}

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