# Limit Rules

• Jul 14th 2013, 06:42 PM
brharrii
Limit Rules
I am having some challenges understanding this problem, I was wondering if someone could help me understand how to approach it?

Suppose that:

L (a) = lim as x -> 0 of (a^x -1)/x

Exists or all a > 0. Assume also that lim x -> 0 a^x =1.

Using limit rules, prove that:

L(ab) = L(a) + L(b)

for a,b> 0

Hint: (ab)^x -1 = a^x(b^x - 1) + (a^x - 1)
• Jul 14th 2013, 07:27 PM
chiro
Re: Limit Rules
Hey brharrii.

Have you tried just evaluating the limits for L(a), L(b) and L(ab)?
• Jul 14th 2013, 09:35 PM
brharrii
Re: Limit Rules
Hi Chiro,

Thanks for the response. I'm not all the way sure how I to do that. To be honest I'm not sure that I understand the question completely. I understand the concept of a limits, but this question is quite a bit different from the ones I've been working on in the past. I'm used to solving limits where there is only 1 variable. How Can this problem be evaluated with so many variables? (a, b, x)

Thanks!
• Jul 14th 2013, 09:44 PM
chiro
Re: Limit Rules
Given an expression for L(x) sub in x = a, x = b, and x = ab and then show that LHS = RHS (in terms of L(ab) and L(a), L(b)).