Evaluate the limit, if it exists.

Question

Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)

lim x→−4 x + 4

x3 + 64

 

Answer 1

a^3 + b^3 = (a+b)(a^2 - ab + b^2)

Thus, (x+4)/(x^3+64) = (x+4)/((x+4)(x^2-4x + 16)) = 1/(x^2-4x+16) for x not equal to -4

Thus, lim x -> -4 1/(x^2 - 4x + 16) = 1/((-4)^2-4(-4)+16) = 1/48