limit help

Question

Find the limit of the function algebraically.

Answer 1

lim  (x^2-36)/(x+6)

x-->-6

x^2-36 =(x+6)(x-6)

lim  (x+6)(x-6)/(x+6)

x-->-6

lim  (x-6)

x-->-6

Apply the limits

-6-6 =-12

Therefore,

lim  (x^2-36)/(x+6)   =-12.

x-->-6