`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.

Expert Answers
gsarora17 eNotes educator| Certified Educator

`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`

scisser | Student

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`