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Limits Continuity and Differentiability question

2022 · 30 Jun · Shift 1 · Q35

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JEE Main
Mathematics
Limits Continuity and Differentiability
2022 · 30 Jun · Shift 1 · Q35

Limits Continuity and Differentiability question

2022 · 30 Jun · Shift 1 · Q35

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

Suppose

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

exists and is equal to L, where

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

. Then,

-

112 L is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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