I do understand that is the number such that

and how it is obtained.

But I don't understand how the definition of the function as a limit of a sequence is obtained, i.e.

Is there a proof?

Appreciate those who help. Thanks!

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- July 1st 2009, 02:27 AMacc100jtDefinition of exponential functions
I do understand that is the number such that

and how it is obtained.

But I don't understand how the definition of the function as a limit of a sequence is obtained, i.e.

Is there a proof?

Appreciate those who help. Thanks! - July 1st 2009, 02:34 AMsimplependulum
We can expand it by Binomial Theorem

By taking the limit , n tends to infinity ,

- July 1st 2009, 02:50 AMacc100jt
great, thanks!