Help Solving the Limit of this equation (third root)

Find the solution for: [(1+cx)^1/3 - 1]/x as x approaches 0.

Hello, I've been trying to solve this problem for a little over a month without much progress.. (Doh)

Looking at it, the logical answer seems to be to get the (1+cx) out of it's third root form to cancel the constants and remove x, but I can't seem to do that w/o adding other similar terms. I've tried adding elements to the top to get a factorial out but that hasn't worked, I've tried multiplying by the positive counterpart ((1+cx)^1/3 + 1) to up the polynomial without luck, and lately I've been playing with natural logs to bring the 1/3 down; all to no avail.

I know the limit exists for sure, any help would be appreciated.

Thanks,

Rhek

Re: Help Solving the Limit of this equation (third root)

Re: Help Solving the Limit of this equation (third root)

I've never like using "L'Hopital" if a limit could be done without Calculus.

Recall that

Taking y= 1,

Replacing x by , and and

That is, can be written as

And, the limit of **that**, as x goes to 0, is easy.

Re: Help Solving the Limit of this equation (third root)

Thanks for both the responses guys. I should have stipulated that the problem is meant to be done w/o the use of derivatives, but now I/ve got both solutions. Thanks so much for the help, been scratching my head over that one for a long time.

-Rhek