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Numerade Educator

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Problem 20 Easy Difficulty

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.

$ \displaystyle \lim_{x\to \infty} \frac{x + x^2}{1 - 2x^2} $

Answer

$-\frac{1}{2}$

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Video Transcript

So for this problem here we're looking at X plus X squared. Provided by one minus two X squared. That's our function. And we see that if we plug in infinity we would get infinity over negative infinity. And that's considered an indeterminate form. So instead what we can do is take the derivative of the numerator and we would get to acts Then we take the derivative of the denominator. We get a -4 X. And we plug in infinity. We're going to get infinity over negative infinity. So this is going to be yet another and determinant form. That's no problem because we can use the hotel's rule again, taking the derivative of the numerator this time we'll get to and then the derivative of the denominator here will get negative four. That would just be a negative one half. So when we take the limit of a constant value, it's just going to be that constant value. So our limit is negative .5