A) \[0\]
B) \[1/2\]
C) \[\frac{1}{4}\]
D) \[-\frac{1}{2}\]
E) None of these
Correct Answer: A
Solution :
Given, \[f(x)=\left\{ \begin{matrix} \frac{1-\cos x}{x}, & x\ne 0 \\ k, & x=0 \\ \end{matrix} \right.\] \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=\underset{x\to 0}{\mathop{\lim }}\,\frac{1-\cos x}{x}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{2{{\sin }^{2}}\frac{x}{2}}{4\left( \frac{x}{2} \right)}.x=0\]and\[f(0)=k\] \[\because \]Function is continuous at\[x=0\]. \[\therefore \] \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=f(0)\Rightarrow k=0\]You need to login to perform this action.
You will be redirected in
3 sec