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  4. Let f(x) =|x| cos (1 /x) +15x2,x ≠ 0 =k,x =0

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

Solution:

$\lim_{x\to0} f\left(x\right) = \lim _{x\to 0} \left(\left|x\right|\cos \frac{1}{x} +15 x^{2}\right) = 0 + 0= 0$
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