Question

How do you find the limit of `(x - (1/x))^2` as x approaches infinity?

Answer 1

`lim_(xrarroo)(x-1/x)^2=oo`

Explanation:

We have:

`lim_(xrarroo)(x-1/x)^2`

As `x` approaches infinity, `1/x` approaches `0`. The `x` remains unboundedly increasing as `x` approaches infinity, so the limit goes to infinity as well.

`=lim_(xrarroo)(oo-0)^2=oo`

In fact, as `x` approaches infinity and `1/x` gets closer and closer to `0`, the function begins more and more to resemble `(x-0)^2=x^2`, the parabola.

`y=(x-1/x)^2`:

graph{(x-1/x)^2 [-31.73, 33.22, -1.92, 30.57]}

`y=x^2`:

graph{x^2 [-31.73, 33.22, -1.92, 30.57]}