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

  • Thread starter myanmar
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
86
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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?

Sum the first answer and that and you'll have your answer.

Don't use software for this, trust me--you'll only be hurting yourself in the long run. Wrap your head around it conceptually.
 
  • #3
33
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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.

Thanks for your help, I've got the answer now.
 
  • #4
263
1
The fastest way is first evaluating x^(-1/3), as x approaches infinity, is obviously equal to zero. Then, you're left with +2x, which is obviously infinity.
 

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