Question

How do you evaluate the limit `(x^4+5x^3+6x^2)/(x^2(x+1)-4(x+1))` as x approaches 1?

Answer 1

Plugging in `1` yields `-2.`

Explanation:

Simply plug `1` into the limit to determine whether we will end up with an indeterminate form (I.E. `0/0`) which will require further simplification.

Generally, plugging in the value you're approaching is the first step you should take when working with a limit unless you know beforehand you'll be working with an indeterminate form:

`lim_(x->1)(x^4+5x^3+6x^2)/(x^2(x+1)-4(x+1))=(1^4+5(1^3)+6(1^2))/(1^2(1+1)-4(1+1))=12/(2-8)=-12/6=-2`

So, the limit is equal to `-2` and no further simplification is necessary.