Calculus limit question, help!?

Question

Help me evaluate this, I know the answer but I don't know how to get to it.

lim (1/4 + 1/x) / 4+x

x>-4

Answer 1

if it is x>-4 the limit is 0

but if you ment to say find the limit as x approaches 4 (x-> 4) the limit is .0625 or 1/16

Answer 2

Use l'Hopital's rule.  This gives -x^2/1, which is defined at x = -4.

Answer 3

lim (1/4 + 1/x) / (4+x)

x --> -4

When you plug it in you get 0/0 which is an indeterminate form. Using L'Hopital's rule you get

lim (1/4 + 1/x) / (4+x)

x --> -4

is the same as

lim (-1/x^2 )

x --> -4

which equals -1/16