Question

Find the limit of the function algebraically. x→−3 (x^2-9/x^3+3)

a) -6
b) -3
c) does not exist
d) 0

Answer 1

d) 0

Explanation:

The function is defined for x=-3, so it can simply be evaluated there.

`\displaystyle\lim_(x \to -3)\left((x^2-9)/(x^3+3)\right)=((-3)^2-9)/((-3)^3+3)=(9-9)/(-27+3)=0`