1. Limit proof

Could anyone give me some advice on this proof?

prove that the limit as h goes to zero ((ab)^h-1)/h= limit as h goes to zero (a^h-1)/h+limit as h goes to zero (b^h-1)/h

this may be easier sorry

2. Re: Limit proof

edit: I see this problem counts toward your grade...did your instructor say it is okay to get outside help?

3. Re: Limit proof

we can go to the math center at our school for help. I was at the math center tell 9 when they closed and i have two problems left this being one of them. I doubt that he would care because the math center will just help you work through the problems.

4. Re: Limit proof

I don't mean to be a stickler, but I find it strange that a professor would give graded problems and allow you to go to the math center to get assistance with them...to me this looks like a take home test problem. When I was a student, it was clearly understood that we were to get no assistance of any kind on our tests, take home or otherwise. The tests were meant as a means of assessing our ability to work problems without assistance.

I just feel uncomfortable knowingly helping with a graded problem.

5. Re: Limit proof

Two suggestions...

1) L'Hôpital's rule.

2) Show both sides have the same limit.

6. Re: Limit proof

I think that covers about all we can do for a graded assignment.

-Dan

7. Re: Limit proof

Originally Posted by ethandf06
Could anyone give me some advice on this proof?

prove that the limit as h goes to zero ((ab)^h-1)/h= limit as h goes to zero (a^h-1)/h+limit as h goes to zero (b^h-1)/h

this may be easier sorry
here is a hint (if you know how to use it):

For small $\varepsilon$ we have $e^\varepsilon=1+\varepsilon +O(\varepsilon^2)$.

.