12.4 Limits of Infinity

Limits of Infinity are basically asking about the horizontal asymtote. In order to find the solution to a limit as it aproaches infinity, we just need to find the horizonatal asymtote.

Finding the horizontal asymtote is basically finding where the graph will go when x becomes REALLY big.

When x becomes really big, only the first term is significant. Anything after that is so minor that it won't factor into changing the final answer, so it can just be disreguarded.

When the powers of x are the same, you are adding the same amount to both the numerator of the equation and the denominator so the ration of the x value will remain the same, so the horizontal asymtote is the ratio of the x's.

When the Power of x in the numerator is greater than the power of x in the denominator, the function will continue to increase forever, not approaching any horizontal asymtote, so therefore, the asymtote doesn't exist.

When the power of x in the numerator is less than the power of x in the denominator the horizontal asymtote is zero because the bottom will continue to become bigger and bigger, creating a smaller and smaller fraction, thus approaching zero.

To find solutions to limits as x approaches infinity, go to wolframalpha