Question

How do you prove that the function `f(x) = [x^2 + x] / [x]` is not continuous at a =0?

Answer 1

Check below

Explanation:

`f` is not continuous at `0` because `0` `cancel(in)` `D_f`

The domain of `(x^2+x)/x` is `RR`* `=RR-{0}`

Answer 2

Expression undefined; `0` in denominator

Explanation:

Let's plug in `0` for `x` and see what we get:

`(0+0)/0=color(blue)(0/0)`

What I have in blue is indeterminate form. We have a zero in a denominator, which means this expression is undefined.

Hope this helps!