Question

calculate the limit:
limx→10− (x^2−100)÷|x−10|

Answer 1

I am assuming you intend\[\lim_{x\rightarrow 10^-}\dfrac{x^2-100}{\left|x-10\right|}\]When x<10, the denominator is equivalent to -(x-10), thus, with a factored numerator, we have:\[\lim_{x\rightarrow 10^-}\dfrac{(x+10)(x-10)}{-(x-10)}=\lim_{x\rightarrow 10^-}-(x+10)=-20\]For more solutions to textbook problems, be sure to check out http://www.slader.com/s/eWFrZXlnbGVl. I submit a lot of content there as well.

Answer 2

great explanation! thanks.