Question

How do you find the graph of `y=xcos(1/x)`?

Answer 1

See below

Explanation:

`y=xcos(1/x)`

For large `x`, `y -> x` so for large `x` the graph tends to `y=x`

However, as `x` approaches 0 from below and above the graph oscillates with ever greater frequency and diminishing amplitude.

The limit of `y` as `x->0 = 0`.

We can see these features from the graphs of `y` below.

graph{xcos(1/x) [-0.6537, 0.6786, -0.327, 0.339]}

graph{xcos(1/x) [-28.85, 28.86, -14.43, 14.45]}