Answer to Question #109584 in Calculus for Alamin

Question

Find the limit. (If an answer does not exist, enter DNE.)
lim
x→4
x − 4
x2 − 16
STEP 1: Factor the denominator.
lim
x→4
x − 4

x + 4


x −




STEP 2: Simplify.
lim
x→4
1
x +


STEP 3: Use your result from Step 2 to find the limit.
lim
x→4
x − 4
x2 − 16
=

Answer 1

$\lim_{x\to 4}\frac{x-4}{x^2-16}=\lim_{x\to 4}\frac{x-4}{(x-4)(x+4)}=$

$=\lim_{x\to 4}\frac{1}{x+4}=\frac{1}{8}=0.125.$