Question

How do you find the limit of `(x cos (1/x))` as x approaches `oo`?

Answer 1

See below.

Explanation:

As `xrarroo`, we have `cos(1/x)rarr1`. And for `x` sufficiently great (`x > 2/pi`) , we have `0 < cos(1/x)`, so

`co(1/x)` is positive and approaching `0`.

As `x` increases without bound, `xcos(1/x)` approaches `x` which is (of course) increasing without bound.

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