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

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

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