Find the limit below.

Question

Find the limit below.

 

limτ(x→3) (x^4−81)/(x−3)

 

 

Answer 1

Reduce the fraction:

 

(x⁴ - 81)/(x - 3) = (x² - 9)(x² + 9)/(x - 3) = (x - 3)(x + 3)(x² + 9)/(x - 3) = (x + 3)(x² + 9).

 

This is necessary because the function is discontinuous at x = 3 and the limit cannot be found by simply plugging in x = 3 (you'll get 0/0).

 

Then

 

lim_x→3 (x + 3)(x² + 9) = (6)(18) = 128.