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### Course: Differential Calculus>Unit 1

Lesson 2: Estimating limits from graphs

# Connecting limits and graphical behavior (more examples)

Sal analyzes various 1- and 2-sided limits of a function given graphically. Created by Sal Khan.

## Want to join the conversation?

• What is the point of taking a limit? What would be its application to everyday life? I seem to understand how it all works mathematically, but I don't understand WHY we use them.
• As someone who never liked maths much in high school, I can totally understand where you're coming from - but now as an adult studying maths at university I can affirm that pretty much everything you learn in maths is relevant, probably in ways you've never though of.
For example at our institution we are using math to do in silico trials. These are medical trials performed by a computer using software to run our equations to emulate/simulate a real trial. Using derivatives and limits we can look at how tumors grow in a particular type of cancer, to better understand the relationship between our immune system and cancer cells.
• What's the difference between 1) limit does not exists
2) limit undefined
• You say does not exist when dealing with the limit.(ex:lim f(x))
You say undefined when dealing with a function alone(ex:f(x))
At least that is how my calculus teacher explains it.
• At , when the tutor was explaining why it is false, can someone give a bit more of a explanation on why it is false cause I'm looking at the graph and I keep coming up with zero.
• I don't believe Sal actually made a mistake. He states that we are coming from the positive side, so we would approach from numbers greater than 1. At those numbers it appears that we approach 1, as he stated. If we had approached from the negative side then yes, we would be approaching 0. I believe you mistook the positive sign as a sign to go up the number line. That would explain why you are coming from the negative side.
• does the last example also mean that "limit exists at 1 as x approaches to 1.5?"

I mean if there is no sign to decide which side we approach from, It asks whether limit exists(so we should check from both sides)?
• Yes, you should check from both sides.
(1 vote)
• Shouldn't the limit of f(x) as x approaches 1 = 1 because the bubble is filled in for the straight line and not for the curved line?
• That is when you are coming from the right side and not the left.
(1 vote)
• What Happens if you try to take the limit of a side-ways parabola (like x=y^2+y+1)? Would it also be undefined?
• A side-ways parabola is not a function with respect to x, so we do not study its properties using calculus.
• I m struggling with the precise definition of a limit (f(x) - L) < e and can't find a video which helps with this topic. Could anyone help out?
• So the limit as x approaches 0 in this function is 1? Even though we already have a clearly defined y value of "0" for x=0? Does that mean that limits don't take into consideration the actual values for when they reach their "destination"? I'm a little confused.
• The limit as you approach a particular value is what it looks like the function ought to be, which may or may not be what the function actually is at that point. Thus, if the function is continuous, the limit and the function will have the same value. But, if the function is not continuous at that point, there is a sudden change at that point, then the limit will be whatever the function would have been had there been no sudden change.
• Why is it called calculus? I don't understand that.
• "Calculus" is derived from the latin word meaning pebble, because that is what was originally used for calculations.
• If a limit can only be approached from one side such as lim(x->-1) arccos(x) does the limit exist?