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Numerade Educator

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Problem 18 Easy Difficulty

Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to -\infty}\frac{4x^3 + 6x^2 - 2}{2x^3 - 4x + 5} $

Answer

2

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Video Transcript

To evaluate this limit me 1st factor out the variable with the highest exponent for the numerator and variable with the highest exponent for the denominator. That means we have limit as X approaches infinity of in this case the numerator well have X cubed as its variable with the highest exponent. And so we get X cubed times. We have four plus six over X two over X cube. And then this will be divided by um for the nominator. We also have X cube as the variable with the highest exponents. So we have X cubed times two minus, pour over X squared plus five over X to the 3rd power. Now simplifying this, we can cancel out the X cube and we have the limit as X approaches infinity of four plus six over x -2 over X. Cube. That's divided by 2 -4, x squared Plus five over x cubed. Now evaluating at infinity we have four plus six over infinity -2 over infinity over 2 -4 over infinity plus five over infinity. Now Know that a constant over infinity will always approach zero. And so six over infinity will approach zero as well as to over infinity for over infinity and five over infinity. And so we are left with 4/2 which reduces to two. And so this is the value of the limits