Which of the following functions are not defined at $x=0$ / have removable discontinuity at the origin
(a) $f(x) =\frac {1}{1+2^{\cot x}}$
(b) $f(x) =\cos \frac {|\sin x|}{x}$
(c) $f(x) = x \sin \left(\frac\pi x\right)$
(d) $f(x) = \frac{1}{\log|x|}$
According to me (a) and (d) should be the answer as it is not defined at $x=0$ but this doesn't match the answer. What is the way to check removable discontinuty
Hint:
Try to look at the value of $$\lim_{x\to 0} f(x)$$
How do you think this limit is connected to removable discontinuities?