# Show that lim x^(-1/3) +2x as x approaches inf is inf.

## Homework Statement

Show that the limit of h(x), as x approaches infinity is infinity
Given:
x is not equal to 0
Def: h(x)=x^(-1/3) +2x

## Homework Equations

Not sure here. Limit of a sum is the sum of the limits, etc.
I'm stuck within a piece of software. So, I'm able to apply equations that the software lets me.
I believe the software is called Maple, but I'm not sure

## The Attempt at a Solution

I've done a couple of these.
I try going in one direction and get stuck.

So I get to something like
( 1 + 2 ( lim x ^ ( 4/3 ) ) ( lim x ^ ( -1/3 ) )
where both limits are as x->inf

Related Calculus and Beyond Homework Help News on Phys.org
Why can't x be equal to 0?
Also, since the limit is the sum of limits, think about what happens individually to each of
lim (x->inf) x^(-1/3)
Which goes to 0 as x becomes infinitely large. (Think 1 / x^-3) x^-3 always gets larger, so since its in the denominator, it goes to 0.

But what happens when you look at the limit of 2x as x goes to infinity?

Don't use software for this, trust me--you'll only be hurting yourself in the long run. Wrap your head around it conceptually.

The fact that x is not zero is given

I'm only using software because it's required by the course. It allows me to apply valid rules or rewrite expressions in equivalent forms. That's all. It sets limits on me by requiring me to solve problems. It doesn't care how I get to the answer as long I adhere to what it lets me do.