Please help me to find out the following limits.

1. lim {(1+1/x)^x} as x->0

2. lim{(a^x - 1)/x} as x->(+infinity), a>1

Dear friends,

Please try them out without using L'Hopital's rule.

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- August 3rd 2006, 05:10 AMnirmalya basuLimits
Please help me to find out the following limits.

1. lim {(1+1/x)^x} as x->0

2. lim{(a^x - 1)/x} as x->(+infinity), a>1

Dear friends,

Please try them out without using L'Hopital's rule. - August 3rd 2006, 06:04 AMSoroban
Hello, nirmalya basu!

I can help with #1 if you are allowed to use L'Hopital . . .

Quote:

Let

Take logs: .

Let . . . Note that, if , then

We have: .

If , we have the indeterminate form:

. . Hence, we may use L'Hopital.

Then we have: .

Hence: .

Since , then

Therefore: .

- August 3rd 2006, 08:45 AMThePerfectHackerQuote:

Originally Posted by**Soroban**