Question

What is the limit of `(e^(−7x))cos x` as x approaches infinity?

Answer 1

`lim_(xrarroo)(e^(-7x)cosx) = 0`

Explanation:

`cosx` is bounded as `xrarroo` as it flips back and forth between `1 and -1` indefinitely. It is distinctly finite though.

`lim_(xrarroo) e^(-7x) = lim_(xrarroo) 1/(e^(7x)) = 1/oo = 0`

This means we have

`0*lim_(xrarroo)cosx`

As `cosx` is bounded it remains finite and final limit is 0.