Evaluate the common limit I have to assess some limits without using L'Hopital rule, just by definition. So I got: lim_(h->0)((e^h-1)/h). After evaluating it in a Math app, it states that it's just 1 due to the common limit evaluation, but I don't understand why it's 1.

Kaitlin Jacobson

Kaitlin Jacobson

Answered question

2022-12-17

Evaluate the common limit
I have to assess some limits without using L'Hopital rule, just by definition. So I got:
lim h 0 ( e h 1 h ) .
After evaluating it in a Math app, it states that it's just 1 due to the common limit evaluation, but I don't understand why it's 1.

Answer & Explanation

Raiden Wolf

Raiden Wolf

Beginner2022-12-18Added 7 answers

This all depends on how you define of e h is.
If you know the power series ( e h = n = 0 h n n ! ), it is easy.
If you know that ( e h ) = e h , then e h 1 = 0 h e x d x, and you can use the mean value theorem combined with e 0 = 1 and the continuity of e h to get the result.
There are likely a few other methods, but these came to me.

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