If [ _x 0 ^ - 1x - ^ - 1x 3x^3] is equal to L, then the value of (6L + 1) is

Question

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

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

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

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

Solutions · 1