Question

Let f(x) =|x| cos$\frac{1}{x}+15x^2,x\ne 0=k,x=0$

• A. 15
• B. -15
• C. 0
• D. 6.

Answer 1

Answer: (C)

${\lim }_{x\to 0}f\left(x\right)={\lim }_{x\to 0}\left(\left|x\right|\cos \frac{1}{x}+15x^2\right)=0+0=0$
Also $f\left(0\right)=k$
$\therefore$ ${\lim }_{x\to 0}f\left(x\right)=f\left(0\right)\Rightarrow 0=k$
$\therefore$ $f\left(x\right)$ is continuous at $x$ = 0 if $k$ = 0