Question

How do you find the limit of `f(x) = (x^2 + x - 6) / (x + 3)` as x approaches 0?

Answer 1

-2

Explanation:

`lim_(x rarr 0) (x^2+x-6)/(x+3)=(0^2+0-6)/(0+3)=-6/3=-2`

There is no indetermination. Maybe you have made a mistake.

Did you mean

`lim_(x rarr -3) (x^2+x-6)/(x+3)`

that in fact gives `0/0`?

Calculate the division of `x^2+x-6` by `x+3` which gives `x-2`.

`lim_(x rarr -3) (x^2+x-6)/(x+3)=lim_(x rarr -3)((x-2)cancel((x+3)))/cancel(x+3)=lim_(x rarr -3) (x-2)=-3-2=-5`