Calculus help, please! What does it mean as x of f(x) approaches infinity and the limit approaches infinity?
What does it mean as x of f(x) approaches infinity and the limit approaches infinity?
What does it mean as x of f(x) approaches infinity and the limit approaches infinity?
xyzzy
Favorite Answer
lim f(x) = L
x--> infinity
As x gets bigger f(x) converges on L
Pick some number N
if x> N
|f(x) - L| is small.
lim f(x) = infinity
x--> a
says something else entirely
This says that f(x) gets to be arbitrarily large as x get close to a.
you could think of the lim x--> infinity as asking if there is a horizontal asymptote
and if the lim x-->a = infinity is saying that there is a vertical asymptote.
this simplification doesn't cover all of the possibilities, but it should give you some intuition.
Mathgirl
It means that as you put larger and larger numbers in place of x, the function itself gets larger. It helps to actually try putting in numbers and seeing it for yourself, I feel.
Anonymous
As x gets bigger than any number you can name, so does f(x).