QJEEM21Mad4f5: JEE Main 2021 Mathematics - Class 12 JEEM21Mad4f5 Solution: If is equal to L, then the value of (6L + 1) is

Question

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If

\mathop {\lim }\limits_{x \to 0} {{{{\sin }^{ - 1}}x - {{\tan }^{ - 1}}x} \over {3{x^3}}}

is equal to L, then the value of (6L + 1) is

Accepted Answer

L = \mathop {\lim }\limits_{x \to 0} {{\left( {x + {{{x^3}} \over 6} + .....} \right) - \left( {x - {{{x^3}} \over 3}.....} \right)} \over {3{x^3}}}

L = {1 \over 3}\left( {{1 \over 6} + {1 \over 3}} \right) = {1 \over 6}

\therefore

6L + 1 = 6.{1 \over 6} + 1 = 2

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