If the function f defined on (6,3) by f(x)=cases√2 x-1 x-1, & x4, & x=4cases is continuous…

Question

If the function $f$ defined on $\left(\dfrac\pi6,\dfrac\pi3ight)$ by $f(x)=\begin{cases}\dfrac{\sqrt2\cos x-1}{\cot x-1}, & x
e\dfrac\pi4\k, & x=\dfrac\pi4\end{cases}$ is continuous, then $k$ is equal to:

Accepted Answer

By L'Hopital's rule: $\displaystyle\lim_{x	o\pi/4}\frac{\sqrt2\sin x}{\csc^2x}=\frac{\sqrt2\cdot\frac{1}{\sqrt2}}{2}=\frac12$.

Solutions · 1