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

1 Answer
Mar 21, 2018

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.