Split - Simplifying functions - limits

[SarahWalsh]

Hello im having a lot of trouble with simplifying this limit. I was hoping someone could help me.

Lim (x^(1/3)-1)/(x^(1/2)-1)
x>1

 

[Deleted member 4993]

Hello im having a lot of trouble with simplifying this limit. I was hoping someone could help me.

Lim (x^(1/3)-1)/(x^(1/2)-1)
x>1

Hint; Substitute

\(\displaystyle x \ = \ u^6\)

 

[SarahWalsh]

My teacher already gave me that and im still not sure how to go about it.

 

[mmm4444bot]

What else have you done, so far, that you have not disclosed ?

 

[SarahWalsh]

I multiplied the limits by the congegate of the top and then substituted the U in but i dont know what else to do after i substitute.

 

[Deleted member 4993]

I multiplied the limits by the congegate of the top and then substituted the U in but i dont know what else to do after i substitute.

No - do the substitution first - multiplying by conjugate will not be necessary. You'll neeed to use following formula to continue:

\(\displaystyle a^2 \ - \ b^2 \ = \ (a+b)(a-b)\)

and

\(\displaystyle p^3 \ - \ q^3 \ = \ (p-q)(p^2 + pq + q^2)\)

 

[mmm4444bot]

I multiplied the limits

This must be a typographical error; I see only one limit.

by the congegate of the top and then substituted the U in

Try making the substitution first. That leads to a difference of squares, in the numerator, and a difference of cubes, in the denominator.

Factor top and bottom, and simplify.

Then you could reverse the u-substitution, using u = x^(1/6).

I'm thinking that the limit can be evaluated directly, at this point.