Question

How do you evaluate the limit `-(x^2-3x)/(x-3)` as x approaches `3`?

Answer 1

`lim_(x rarr 3) -(x^2-3x)/(x-3) = -3`

Explanation:

`lim_(x rarr 3) -(x^2-3x)/(x-3) = lim_(x rarr 3) -(x(x-3))/(x-3)`
`lim_(x rarr 3) -(x^2-3x)/(x-3) = lim_(x rarr 3) (-x)`
`lim_(x rarr 3) -(x^2-3x)/(x-3) = -3`

Which we can confirm graphically;
graph{-(x^2-3x)/(x-3) [-10, 10, -5, 5]}