Infinite Limit

krystaline86 · #1 $Old$ October 24th, 2008, 07:27 PM

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?

Chris L T521 · #2 $Old$ October 24th, 2008, 07:33 PM

Quote:

Originally Posted by krystaline86 $View Post$

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. $\frac{1}{\pm\infty}=0$ , whether if it was $+\infty$ or $-\infty$ .
= 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 $\lim_{x\to-\infty}x^3-\frac{1}{x^3}$ , we see that as $x\to-\infty$ , $x^3\to-\infty$ ; and as $x\to-\infty$ , $-\frac{1}{x^3}\to 0$ , thus the limit would equal $-\infty+0=\color{red}\boxed{-\infty}$

Does this clarify things?

--Chris