F x -sin x - x- n- -n-0- 1- 2- 3- 2 - otherwise and g x - x 2 -1 - x- 0 4 - x-0 - Then lim x- 0 g f x is

The correct option is C 5 lim _ x→ 0 g( f( x ) #160; ) #160; =g( f( 0 ) #160; ) =g(2)= 2 ^ 2 +1=5 ...

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Differentiation under Integral Sign

f x =sin x ...

Question

$f (x) = {\begin{matrix} sin x; x \neq n π, n = 0, \pm 1, \pm 2, \pm 3..... 2; o t h e r w i s e \end{matrix}$ and $g (x) = {\begin{matrix} x^{2} + 1; x \neq 0 4; x = 0 \end{matrix} .$
Then ${lim}_{x \to 0} g (f (x))$ is

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