# If the function is continuous at each point in its domain and thne k is _________. Option: 1 3 Option: 2 4 Option: 3 5 Option: 4 6

\begin{aligned} &\lim _{x \rightarrow 0} \frac{\cos (\sin x)-\cos x}{x^{4}}=f(0) \\ &\Rightarrow \lim _{x \rightarrow 0} \frac{2 \sin \left(\frac{\sin x+x}{2}\right) \sin \left(\frac{x-\sin x}{2}\right)}{x^{4}}=\frac{1}{K} \\ &\Rightarrow \lim _{x \rightarrow 0} 2\left(\frac{\sin x+x}{2 x}\right)\left(\frac{x-\sin x}{2 x^{3}}\right)=\frac{1}{K} \\ &\Rightarrow 2 \times \frac{(1+1)}{2} \times \frac{1}{2} \times \frac{1}{6}=\frac{1}{K} \\ &\Rightarrow K=6 \end{array}

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