JEE Main 2021 (Online) 17th March Morning ShiftQuestion 1
If the function $f(x)=\frac{\cos(\sin x)-\cos x}{x^{4}}$ is continuous at each point in its domain and $f(0)=\frac{1}{k}$, then $k$ is $\_\_\_\_\_\_$ .
Limits & Continuity
Answer$6$
Solution
Using $\cos A-\cos B=-2\sin\frac{A+B}{2}\sin\frac{A-B}{2}$ and series: $\cos(\sin x)-\cos x$ has leading term $x^4/6$. So $f(0)=\frac16=\frac1k\Rightarrow k=6$.