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.
Hello, nirmalya basu!
I can help with #1 if you are allowed to use L'Hopital . . .
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: .