`lim_(t->0) (8^t - 5^t)/t` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply,...

`lim_(t->0) (8^t - 5^t)/t` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.

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Chapter 4, 4.4 - Problem 22 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`lim_(t->oo)(8^t-5^t)/t`

Apply L'Hospital rule, Test condition:0/0

`=lim_(t->oo)((8^t-5^t)')/(t')`

`=lim_(t->oo)(8^tln(8)-5^tln(5))`

plug in the value,

`=8^0ln(8)-5^0ln(5)`

`=ln(8)-ln(5)`

`=ln(8/5)`

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