1. ## Infinite Limit

Okay, so I'm having trouble with subbing in (-)infinity...
a) lim x -> -inf. 1/x^3
= 1/(-inf.)^3
= 1/(-inf.)
= -1/inf.
= 0
Right?
Then consider this...:
b) lim x-> -inf. -1/x^3
= -1/(-inf.)^3
= -1/(-inf.)
= 1/inf. <--- 1) Do the (-)s cancel eachother out here?
= 0
Right?
Now let's say this was part of a bigger eqn such that the eqn looked like:
lim x-> -inf. of f(x)=(x^3)-1/(x^3)
2) Would I have added the zero in my b example, taken it away,
3) Or furthermore, would it be a 0- or 0+?
4) Does it matter since it's a zero and therefore it wouldn't affect the result?

2. Originally Posted by krystaline86
Okay, so I'm having trouble with subbing in (-)infinity...
a) lim x -> -inf. 1/x^3
= 1/(-inf.)^3
= 1/(-inf.)
= -1/inf.
= 0
Right?
Then consider this...:
b) lim x-> -inf. -1/x^3
= -1/(-inf.)^3
= -1/(-inf.)
= 1/inf. <--- 1) Do the (-)s cancel eachother out here? I don't think it would really matter if it was negative or not. $\displaystyle \frac{1}{\pm\infty}=0$, whether if it was $\displaystyle +\infty$ or $\displaystyle -\infty$.
= 0
Right?
Now let's say this was part of a bigger eqn such that the eqn looked like:
lim x-> -inf. of f(x)=(x^3)-1/(x^3)
2) Would I have added the zero in my b example, taken it away,
3) Or furthermore, would it be a 0- or 0+?
4) Does it matter since it's a zero and therefore it wouldn't affect the result?
In evaluating $\displaystyle \lim_{x\to-\infty}x^3-\frac{1}{x^3}$, we see that as $\displaystyle x\to-\infty$, $\displaystyle x^3\to-\infty$; and as $\displaystyle x\to-\infty$, $\displaystyle -\frac{1}{x^3}\to 0$, thus the limit would equal $\displaystyle -\infty+0=\color{red}\boxed{-\infty}$

Does this clarify things?

--Chris