Limits and Limit Laws in Calculus

In introducing the concept of differentiation, we investigated the behavior of some parameter in the limit of something else approaching zero or infinity. This concept of limits is how calculus got started. As the field developed, new techniques arose such that we don't have to find limits very often anymore, but we still use them sometimes, so let's make sure we know what they are, how they work, and how to evaluate them!

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[jashansehgal]

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Please do not leave this channel ever
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[crofregernish]

Trying to do calculus online for a college course where the professor only teaches what's literally in the book (no further explanations)
This was so helpful!!!

[melontusk]

I've been wondering about why the formal definition of a continuous involves a limit for such a long time, and the epsilon-delta definition didn't help either, but this video lecture really made it crystal clear to me. Thanks so much.

[billcook]

Random trivia: One of the examples in this video is that limit x-> 0 of sin(x)/x = 1. Seems simple here using a graph or calculator, but this is one of the most important “facts” in all of math. Not necessarily in this form, but in equivalent forms such as the idea that if x is “small”, sin(x) is approximately equal to x.

[tomsdailystudy]

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[jonathanjohnny]

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[typalfi]

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[Kiky_MedPhysicist]

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[lakewobegonesbest]

Such an easier way to understand, thank you

[GavinLon]

This is a very clear explanation. Thanks Professor Dave.

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[supercheese]

this might be weird to comment on a calculus video but I only passed Further Linear Algebra because of your videos.
Just wish I watched this playlist before my calculus exam.

[MOizSUAVE]

dang i wish i watched this video before my 1st exam.

[barcinnicrab]

Amazing explanation really nice to hear :) Everything makes sens

[RazorM]

People who disliked this video have no limits

[robertwood]

8:45 Lim f(x)=6
Lim g(x)=2
Then it goes to lim[f(x)-3g(x)] =6-3(2)=0
Why is g(x) now being multiplied by 3, instead of 6-2=4?

[MathCuriousity]

I have to say Dave used the word parameter incorrectly; this word means either a constant such as a particles mass, or it can mean a function of two other functions such as if we parametrized the unit circle for t and said y=sin(t) and x=cos(t)