Question

How do you find the limit of `x^2-2x` as x approaches 2?

Answer 1

Informally, we can reason as follows.

Explanation:

As `x rarr2`, we have `x^2 rarr4`

As `x rarr2`, we have `2x rarr4`

Therefore,

as `x rarr2`, we have `x^2-2x rarr 4-4`, which is `0`

`lim_(xrarr2)(x^2-2x) = (2)^2-2(2) = 4-4=0`