Question

Please help me with the below question.

Answer 1

The limit does not exist.

cos is continuous, so we have

`\displaystyle \lim_(x\to0) \cos\left(\frac1x\right) = \cos\left(\lim_(x\to0) \frac1x\right)`

but

• 1/x approaches +∞ as x approaches 0 from above

• 1/x approaches -∞ as x approaches 0 from below

hence the two-sided limit does not exist.