L'Hospital's Rule application problem

[Sczisnad]

Homework Statement

Use l'Hospital's Rule when necessary (you may not need to use it at all). Find the limit.

lim as x approaches 1 of (x^a-1)/(x^b-1)

Homework Equations

The Attempt at a Solution

Ok well, if you sub in 1 for all the x values you get an indeterminate 0/0 i believe because any power to the base 1 is one. Therefor i apply l'Hospital's Rule.

This gives me (ax^(a-1))/(x^(b)-1)-(bx^(b-1)(x^(a)-1))/((x^(b)-1)^(2))

Still indeterminate... If i take the derivative again the problem gets huge and i feel like i am getting farther away from the answer.

 

[Dick]

l'Hopital's rule says to take the derivative of the numerator and divide by the derivative of the denominator. You seem to be taking the derivative of the quotient using the quotient rule. That's not what you want to do.

 

[Sczisnad]

Ah that makes more sense, so all that I would have to do then is find the limit as x approaches 1 of ax^a-1/bx^b-1 which is a/b. so a/b is my answer.

 

[Dick]

Ah that makes more sense, so all that I would have to do then is find the limit as x approaches 1 of ax^a-1/bx^b-1 which is a/b. so a/b is my answer.

That does make more sense.