Is to simplify the problem by just thinkingĪbout which terms are going to dominate the rest. It, or try it out with numbers to verify that for yourself. The horizontal asymptote in this case, is Just as 1 over x, as xĪpproaches negative infinity, gets us close to 0. And what's this going to be? Well, if the denominator,Įven though it's becoming a larger and largerĪnd larger negative number, it becomes 1 over a very, Limit as x approaches negative infinity of 1 over 2x. The fourth, as x approaches negative infinity.
Same thing as the limit of 3x to the third over 6x to Larger and larger? As x gets larger in magnitude. X approaches infinity, in all of this craziness. Which is going to beĮqual to the limit as x approaches infinity. Limit is going to be the same thing as this limit. To be roughly equal to 9x to the seventh overĮspecially since, as we get larger and largerĪs we get closer and closer to infinity, these So at infinity, as we getĬloser and closer to infinity, this function is going Than an x to the fifth term, and definitely much faster And in the denominator,ģx to the seventh is going to grow much faster The 9x to the seventh is going to grow much faster In the numerator, out of these three terms, Seen in other examples, is just to realize which So what's going to happenĪs x approaches infinity? And the key here, like we've
#To infinity and plus
The seventh plus 1,000x to the fifth, minus Minus 17x to the sixth, plus 15 square roots of x. In order for a limit to exist it must approach the same thing from both sides.įinding the limit of functions as x approaches infinity It would be the same as saying that a limit that approaches 3 from the positive side and 2 from the negative side also doesn't exist. So you see, if a limit approaches positive infinity from one side, and negative infinity from the other side… it doesn't approach the same thing from both sides. Think of the biggest positive number you can think of, and then go even bigger than that… and keep doing that… FOREVER! That's positive infinity.įor negative infinity, think of the most negative number you can think of, and then think of an even more negative number, and keep doing that, FOREVER.
Basically positive infinity means to keep going towards bigger and bigger positive numbers. And here, "ends" is in quotation marks because the number line NEVER actually ends, it goes on forever in both directions. Positive and negative infinity represent the opposite "ends" of the number line.
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