`lim_(x->oo)(x + x^2)/(1 - 2x^2)` 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_(x->oo)(x + x^2)/(1 - 2x^2)` 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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Textbook Question

Chapter 4, 4.4 - Problem 18 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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

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

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

apply infinity properties,

`=(0+1)/(0-2)=-1/2`

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scisser | (Level 3) Honors

Posted on

Using an easier method,

Look at the highest degree terms. Since they are to the same power, now look at the leading coefficients, which is `-1/2`

Therefore,
`lim_(x-gtoo)(x+x^2)/(1-2x^2)=1/-2`

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