If the function f(x)=cases√2+ x-1(-x)^2, & x, & x=cases is continuous at x=, then k equals…

Question

If the function $f(x)=\begin{cases}\dfrac{\sqrt{2+\cos x}-1}{(\pi-x)^2}, & x
e\pi\k, & x=\pi\end{cases}$ is continuous at $x=\pi$, then $k$ equals:

Accepted Answer

Let $	heta=\pi-x	o0$. $\displaystyle\lim_{	heta	o0}\frac{\sqrt{2-\cos	heta}-1}{	heta^2}=\lim_{	heta	o0}\frac{1-\cos	heta}{	heta^2}\cdot\frac{1}{\sqrt{2-\cos	heta}+1}=\frac12\cdot\frac12=\frac14$.

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