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
VNVDVI
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.

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