`lim_(x->1) (x^3 - 2x^2 + 1)/(x^3 - 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...

`lim_(x->1) (x^3 - 2x^2 + 1)/(x^3 - 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 9 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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

`=lim_(x->1)((x-1)(x^2-x-1))/((x-1)(x^2+x+1))`

`=lim_(x->1)(x^2-x-1)/(x^2+x+1)`

plug in the value,

`=(1^2-1-1)/(1^2+1+1)`

=-1/3

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