Question

Evaluate:

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

Answer 1

again apply l'hospitals and u'll get -1/16.

Answer 2

We haven't learned how to hospital's yet.

Answer 3

you need to use l'hopsital's rule to get lim x->-4 (-1/x^2)

Answer 4

l'hosptial is where if u get 0/0 or infinity/infinity you take the derivative of the numerator and the derivative of the denominator seperately and evaluate them at the limit

Answer 5

we have only used the limit laws

Answer 6

Can you show me it's done using the l'hospital law

Answer 7

sure

Answer 8

by using regular limit laws you can see that you will get 0/0 which is not allowed

Answer 9

therefore you use l'hospital which is the derivative of the numerator and the derivative of the denominator

so take d/dx (1/4 + 1/x)

Answer 10

and then d/dx (4+x)

Answer 11

so d/dx (1/4 + 1/x) will get you -1/x^2 since 1/x can be represented as x^-1 and 1/4 is a constant

Answer 12

and the denominator will go to 1

Answer 13

now since its (-1/x^2)/1 you evaluate the limit again at lim x-> -4 to get -1/16

Answer 14

ah... ok i get it a little bit

Answer 15

so in short l'hospital says that lim x->a f(x) = lim x-> a f'(x)
------ -----
g(x) g'x

only when you get a indeterminate which is 0/0 or infinity/infinity

Answer 16

never mind....don't use l'hospital rule here...u take the lcm of the numerator and so u'll end up cancellin the (x+4) term from the fraction. and u'll be left out with only 1/4x wer x->-4
u get the same -1/16 :)