- Limits to infinity: What happens to functions as x gets really, really big?
- Vertical limits: Sometimes y goes off to infinity
- Finite limits: Limits when both x and y stay finite
- One-sided limits: Limits that come from only the left or right side
- Continuity (for real): Dive deeper into continuity, using one-sided limits
- Splitting limits: Tricks for simplifying limits (and when they don't work!)
In this section we will learn about limits whose value is infinity or minus infinity.
The function f(x) will have a horizontal asymptote at y=L if either of the following are true; limit x go to infinity f(x) = L and limit x go to minus infinity f(x) = L.
The function f(x) will have a vertical asymptote at x = a if we have any of the following limits at x = a; limit x approaching a-negative f(x) = positive/negative infinity, limit x approaching a-positive f(x) = positive/negative infinity, and limit x approaching a f(x) = positive/negative infinity.
We say that the limit of f(x) is L as x approaches a and write this as limit x approaches a f(x) = L, provided we can make f(x) as close to L as we want for all x sufficiently close to a, from both sides, without actually letting x be a.
The function would be continuous if you changed the value at one x-coordinate.
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