Suppose lim x → 0 (F(x))/(x³) exists and is equal to L, where F(x) = | a + sin x/2 - b cos x 0 - b cos x 0 a + sin x/2 0 a + sin x/2 - b cos x |. Then, - 112 L is equal to _ _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2022 Mathematics question

JEE Main 2022 · 30 Jun, Morning shift · Q34

JEE Main 202230 Jun, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Suppose

\mathop {\lim }\limits_{x \to 0} {{F(x)} \over {{x^3}}}

exists and is equal to L, where

F(x) = \left| {\matrix{ {a + \sin {x \over 2}} & { - b\cos x} & 0 \cr { - b\cos x} & 0 & {a + \sin {x \over 2}} \cr 0 & {a + \sin {x \over 2}} & { - b\cos x} \cr } } \right|

. Then,

-

112 L is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.