How to solve this limit?

Question

lim = (x^2 - 9x - 10) / (x plus 1)

x->-1

how do you solve this limit in an easy method?

Cheers.

Answer 1

first factorize the top half of the equation

x^2-9x-10 would become (x-10)(x+1)

then you can cancel with the bottom part of the equation

(x-10)(x+1)/(x+1) this leaving (x-10)

then you apply the limit

hope that helps!!

Answer 2

(x^2-9x-10) / (x+1) =

(x+1)(x-10) / (x+1) =

(x-10)

lim x->-1 (x-10) = (-1-10) = -11

Answer 3

x^2 - 9x - 10 = x^2 - 2*4.5x + 4.5^2 - 4.5^2 - 10 =

= (x - 4.5)^2 - 20.25 - 10 = (x - 4.5)^2 - 30.25 = (x - 4.5)^2 - 5.5^2 =

= (x - 4.5 - 5.5)(x - 4.5 + 5.5) = (x - 10)(x + 1)

lim x->-1 (x^2 - 9x - 10)(x + 1) = lim x->-1 (x - 10)(x + 1)/(x + 1) =

= lim x->-1 x-10 = -1 - 10 = -11