Question

Evaluate the limit:
limx-> -3 (1/x + 1/3) / (x+3)

Answer 1

the limit is -1/9

Answer 2

What did you have to do: substitution, rationalization, factoring or change of variable?

Answer 3

do you know lhopitals rule?

Answer 4

nope, I've never heard of that.

Answer 5

if you substitute -3 and get 0/0
you need to use lhopitals rules
u just differentiate the nominater first then the denominator
then substitute -3
when you differentiate 1/x+1/3
you get -1/x^2

and when you differentiate x+3 you get 1
soo
it becomes
limx>-3 (-1/x^2)/1
now substitute x=-3
you get -1/9

Answer 6

lhopitals rule is used when you get 0/0
infinity/infinity
you just differentiate up and down then substitute...
its the easiest

Answer 7

Ohhh okay that makes sense, thank you!

Answer 8

:)