The Derivative in Calculus Defined as a Limit

The Derivative in Calculus Defined as a Limit - [1-2]

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Жыл бұрын

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In this lesson, you will learn what the mathematical definition of a derivative is in calculus. The derivative is defined to be the slope of the line tangent to a function at a point. In order to do this, we find the slope of a line passing through two far away points, then slowing move these points closer together using the limit process. The derivative is then defined to be the slope of the line tangent to the function at a given point, and is calculated to be the slope of the line through two points, as the limit takes these two points to be infinitely close together.

Пікірлер: 39

@khalilfuller4939 4 ай бұрын

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@V21IC 6 ай бұрын

I think that I'm learning Calculus! I saw a feed on Facebook but it was dubios that I had to search for clear teaching on the subject! I think many teachers try to show how 'smart' they are instead of imparting knowledge to be understood by learners. I must say, that you're humble and teaches very well! Your style is like a breaking story that I've never heard in decades!

@83jbbentley Жыл бұрын

Calculus reflects many of the ongoing math problems of the time. -tangent line - area under curve It’s really one of the most amazing breakthroughs of modern man. Like the printing press. Think how costly book were? It’s like YT in a way. Imagine teachers like you who’s impact is so far stretching that most people don’t understand

@MathAndScience Жыл бұрын

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@oddyorozuya6958 Жыл бұрын

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@user-ky5dy5hl4d Ай бұрын

@@MathAndScience What about if we left 5h/h and let h approach zero? We would have 0/0 which is nonsense.

@kwenda Жыл бұрын

All I can say is where were you all these years hahah. Going back to University and stumbled upon this and I can’t stop learning. Thank u.

@biffboffo 9 ай бұрын

I wish I had something like YT in high school in the 80s. I had a calculus teacher who wasn’t very good, and it would’ve helped me tremendously to hear the explanation from someone else.

@Rem91067 3 ай бұрын

Same here. My calculus instructor didn’t like to explain things; he just blew through it all and I couldn’t follow. I ended up dropping the class. Up until then, I had always done well in math. My failure to comprehend calculus really disheartened me and dashed any hope I had of majoring in the sciences.

@hemrajue3434 Жыл бұрын

I think slope definition gives us slope between two discrete points whereas the limit definition of derivative gives us the slope at a point of a continuous curve.

@MathAndScience Жыл бұрын

Very well said!

@V21IC 6 ай бұрын

Couldn't agree more! Thanks!

@V21IC 6 ай бұрын

Damn! I think you just nailed it!🎉🎉 1. Slope(of a curve) - A straight line touching two points along a curve! Any two points in between may have a different slope. 2. Limit - The point on the curve and from which a slope can be derived! Wow! Limit definition is one point along the curve WHERE a slope can be derived! So, when the line touches two points along the curve is a slope. A line touching one point is the limit from which a slope can be 'derived'!

@tresajessygeorge210 3 ай бұрын

THANK YOU... SIR...!!! It is hard to remember... but understands the concept ...!!! THANKS AGAIN...!!!

@sameerpabreja8742 Жыл бұрын

Thank you so much, you are a real exam life saver.

@MathAndScience Жыл бұрын

Happy to help!

@Moroma_ Жыл бұрын

Amazing 👏

@MathAndScience Жыл бұрын

Thank you! Cheers!

@lipingma9016 6 ай бұрын

Well explained !

@sergiomorales4302 Жыл бұрын

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@MathAndScience Жыл бұрын

Awww thanks!

@wilkyclergeot9416 Жыл бұрын

Thank you so much incredible teach for everything!!!

@MathAndScience Жыл бұрын

Thank you!

@user-ky5dy5hl4d Ай бұрын

In the denominator of the derivative definition is h. But it really came from x values of (a+h)-a.

@surajshukla5741 Жыл бұрын

Thanks sir

@matthewgaydos8642 Жыл бұрын

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@MathAndScience Жыл бұрын

Thanks so much!

@drumtwo4seven Жыл бұрын

Nice 👍

@MathAndScience Жыл бұрын

Thank you!

@user-ky5dy5hl4d Ай бұрын

What about if we left 5h/h and let h approach zero? We would have 0/0 which is nonsense.

@gemini22581 7 ай бұрын

Why did u substitute x+h for x???

@ashtesera6949 Жыл бұрын

You are brilliant teacher.

@yuusufliibaan1380 Жыл бұрын

Good lesson thank you ☺️💕

@MathAndScience Жыл бұрын

Welcome!

@augmentedman Жыл бұрын

Thank you Spiderman

@sammin5764 Жыл бұрын

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@kostaskostas2470 5 ай бұрын

It’s a good video but your argument that teaching limits is ridiculous is unfortunate. Calculus is all about limits. Limit is the revolutionary idea that allows calculus to develop. It is sad and not good to see calculus as differentiation and integration and teach the rules.