Question

How do you evaluate the limit of `lim (x^2-3x)/(x^2+2x-15)` as `x->3`?

Answer 1

Factorize the expression.........

Explanation:

`f(x)=(x^2-3x)/(x^2+2x-15)=(x(x-3))/(x^2+2x-15)=(x(x-3))/((x+5)(x-3))`

`=(xcancel((x-3)))/((x+5)cancel((x-3)))` `=` `x/(x+5)`

`f(x)_("lim"xrarr3)=3/8`

Note that this `"limit"` is INDEPENDENT of the value of `f(x)` at `x=3`, which is undefined.