How to find lim (e^t-1)/t as t->0 using l'Hospital's Rule?

Talon Cannon

Talon Cannon

Answered question

2023-03-25

How to find lim e t - 1 t as t 0 using l'Hospital's Rule?

Answer & Explanation

paumEFupbom2lda

paumEFupbom2lda

Beginner2023-03-26Added 6 answers

We have
L = lim t 0 e t - 1 t
To apply L'Hôpital's rule, we must have a 0 / 0 or / situation. If we plug in t = 0 we find that:
L = e 0 - 1 0 = 0 0
So, we can apply the L'Hôpital's rule, which says:
L = lim t 0 e t - 1 t = d d t ( e t - 1 ) d d t t
We know that e x is one of the functions with the property that f ( x ) = f ( x ) , and as - 1 is just a constant, it will vanish when we take the derivative.
L = lim t 0 e t 1 = lim t 0 e t

L = e 0 = 1
Jase Leonard

Jase Leonard

Beginner2023-03-27Added 6 answers

lim t 0 e t - 1 t = D L H ( 0 0 ) lim t 0 e t = e 0 = 1

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