`lim_(t->1) (t^8 - 1)/(t^5 - 1)` 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...

`lim_(t->1) (t^8 - 1)/(t^5 - 1)` 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 21 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`lim_(t->1)(t^8-1)/(t^5-1)`

`=lim_(t->1)((t-1)(t+1)(t^2+1)(t^4+1))/((t-1)(t^4+t^3+t^2+t+1))`

`lim_(t->1) ((t+1)(t^2+1)(t^4+1))/((t^4+t^3+t^2+t+1))`

plug in the value,

`=((1+1)(1^2+1)(1^4+1))/(1^4+1^3+1^2+1+1)`

`=(2*2*2)/5=8/5`

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