Limit as x tends to 1

1. Nov 30, 2008

sara_87

1. The problem statement, all variables and given/known data

evaluate limit as x tends to 1:

(x^(2/3)-2x^(1/3)+1)/((x-1)^2)

2. Relevant equations

3. The attempt at a solution

=lim (x^(1/3)-1)^2/(x-1)^2

what do i do next??
(note, i dont want to use l'hospitals rule)

2. Nov 30, 2008

wimma

......hmmm..... why not?

Attached is my solution.

Attached Files:

• limits_problem.pdf
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112.7 KB
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55
Last edited: Nov 30, 2008
3. Nov 30, 2008

Office_Shredder

Staff Emeritus
Substitute y = x1/3 Then

$$\frac{(x^{1/3}-1)^2}{(x-1)^2} = \frac{(y-1)^2}{(y^3-1)^2}$$

and y3-1 = (y-1)(y2 + y + 1)

4. Nov 30, 2008

wimma

I can't believe that. I worked it out straight away but it took me like 30 mins to make that PDF lol.... i wish i'd known this forum had LaTeX... then I might not have used LyX

Nike: Every day is a competition.

5. Nov 30, 2008

sara_87

Thank you very much wimma and office shredder.
:)

6. Nov 30, 2008

wimma

no problem XD