First, a one sided limit is when you approach a value from a single side. You specify which side you are coming from with a plus or minus over what x is approaching. This is a one sided limit coming from the right side. This is a one sided limit coming from the left. Since the limits from both the right and left are the same.
The limit exists and is equal to what both of the one sided limits are equal to. But what if you had:. The one sided limits are not equal, so the limit as x approaches 1 does not exist. As a side note, positive and negative infinity can be what x is approaching. This has mathematical significance and is frequently used:.
With limits approaching infinity, if infinity ends up in the denominator, then the limit normally equals 0. If you end up with infinity in the numerator and denominator, then you have to see if the highest degree the one with the biggest exponent of x is in the numerator or denominator.
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