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## AP®︎/College Calculus AB

### Course: AP®︎/College Calculus AB>Unit 1

Lesson 3: Estimating limit values from graphs

# Connecting limits and graphical behavior

AP.CALC:
LIM‑1 (EU)
,
LIM‑1.C (LO)
,
LIM‑1.C.1 (EK)
,
LIM‑1.C.2 (EK)
,
LIM‑1.C.3 (EK)
,
LIM‑1.C.4 (EK)
Usually when we analyze a function's limits from its graph, we are looking at the more "interesting" points. It's important to remember that you can talk about the function's value at any point. Also, a description of a limit can apply to multiple different functions.

## Want to join the conversation?

• This may be a bit stupid, but how do you find the limit as x approaches a specific value of a vertical line?
• A vertical line is not a function so you can't take a limit involving one.
• okay so i just did the practice test and it asked me to choose all that applies. It gave me a notation I haven't seen before which was a superscript of a + and a - sign. The lessons never mentioned those things. So I guess now I know that a negative superscript means it's coming from the left and a positive one means it's coming from the right.
• The practice was one of the most frustrating things I have to endure.
• Don't forget, your brain grows through struggle, so be happy about having gone through the experience!
• The test questions show an additional positive or negative sign in some of the limits: x→−2− What does this mean??
​​
• How can we know whether a one-sided limit is the correct answer, or when a two-sided limit is needed?
Waldemar Klassen
• You should always look for a 2 two-sided limit if applicable. By definition, a limit can exist only when the left and right-hand sides are equal. One-sided limits are usually used for checking continuity or determining behavior of the function.
• How limit of f(x) as x approaches pi is possible ? Can we find out limit of an irrational number ?
I believe we must be considering some approximate value like 3.14 etc.
• It sure is possible! The fact that pi is a irrational number doesn't affect the limit/function in anyway. Graphically, of course, you can't tell the limit of f(x) when x approaches pi with accuracy, but if, instead, there was an expression for f(x) you could easily solve the limit and get an accurate number. If the limit of f(x) when x approaches pi was impossible just because pi is an irrational number, there would be infinite impossible limits in this function, since f(x) is defined by real numbers! And that's not true, since pretty much all limits, no matter the value to which x is approaching, are possible in this function.
Hope this helps!
• How do you find the limit x approaches a specific value of a vertical line?
• Those limits do not exist as, in a vertical line, there is a value of x for which you have infinite y values.
• Is it possible to find the limit of a complex number ?
• Yes. Carefully defining and understanding what that means, and exploring the consequences, leads to the branch of math called complex analysis.
• What if there is a piecewise function comprised of two functions that are undefined for K but the whole function approaches the same corresponding value for K from both sides?
Say f(x) = {x if x > 0, (x^2)/2 if x < 0}
f(x) approaches 0 as x does.