Question

What is the limit of `x(cos(1/x))` as x approaches infinity?

Answer 1

`lim_(xrarroo)x(cos(1/x)) = oo`

Explanation:

As `x` increases without bound, `1/x rarr 0`.

The cosine function is continuous at `0`, so

`lim_(xrarroo)cos(1/x) = cos0 = 1`.

We can conclude that, as `x` increases without bound, `xcos(1/x)` also increases without bound.

That is, `lim_(xrarroo)x(cos(1/x)) = oo` .