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Calculus 3: Limits and Continuity (Video #12) | Math with Professor V

Math with Professor V

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Precise definition of a limit for a function of two variables; how to take the limit along various paths for a function of several variables; squeeze theorem; delta-epsilon proofs; converting to polar; definition of continuity for a function of several variables; examples finding where a composition of functions is continuous as well as a piecewise-defined function.

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15 Comments

@mathwithprofessorv Creator 5 days ago Pinned

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@itsme0_5 2 years ago

The way you go through each concept makes it easier to understand because you draw a map in mind and actually teach how to solve the problems. Thank you!

@danielmeza9155 12 days ago

29:46

@Jsund-j7s 1 year ago

Amazing! This made it all clear for me. Thank you.

@patriciabasisty3809 2 years ago

BEST PROF EVER!!!!!💗💗 TY FOR THIS SERIES

@Angela-d5e8j 2 years ago

Thank you so much!

@emirhamarat3287 2 years ago

Excellent.

@sudenureker9233 2 years ago

Really helpful, thank you..

@richardreiter6861 3 years ago

Excellent video I was a little confused after watching Professor Leonard's video and this cleared everything up including the squeeze theorem and Delta epsilon proof

@emilyf9288 4 years ago

this was really helpful! your explanations are really clear

@thesiblings7674 3 years ago

Thank you! So clear

@mphondadza2757 2 years ago

🎉🎉🎉🎉

@kingbeauregard 5 months ago

Oh hai, I've come up with another possible way to go through epsilon delta.

Let's start with a proposition: lines are continuous. If it's a line, the limit as x->a is always going to be f(a). We can count on lines to be continuous.

But what about a function that's more complicated, like sin(x) as x->a? How do we prove it's continuous? Well you know, that sounds like a lot of work, so I'm not going to do it. Instead, I'm going to find a couple of lines that serve as an "envelope" for sin(x) in the vicinity of x=a; since we know that the lines will be continuous (as all lines are) and the function will always be between the lines in the vicinity of x=a, f(x) must therefore approach f(a) as x->a.