JEE Main 202230 Jun, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002Suppose limx→0F(x)x3\mathop {\lim }\limits_{x \to 0} {{F(x)} \over {{x^3}}}x→0limx3F(x) exists and is equal to L, where F(x)=∣a+sinx2−bcosx0−bcosx0a+sinx20a+sinx2−bcosx∣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|F(x)=a+sin2x−bcosx0−bcosx0a+sin2x0a+sin2x−bcosx. Then, −-−112 L is equal to ___________.Your answerType your answer. Integers and decimals are accepted.CheckSkip · show solution
