Definition of the Derivative | Part I
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- Опубликовано: 21 авг 2017
- Description:
One goal for the derivative is to define the notion of a tangent line to a curve. By approximating the slope of the tangent line by a limit of slopes of secant lines, we arrive at the definition of the derivative.
Learning Objectives:
1) Graphically sketch the intuition behind the derivative
2) State the formal definition of the derivative
Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!
Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.
This video is part of a Calculus course taught by Dr. Trefor Bazett at the University of Cincinnati.
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![The Derivative in Calculus Defined as a Limit - [1-2]](/img/1.gif)
Thank you so much for explaining when and how you've cleaned up an expression.
Many instructors don't do this and while it may seem trivial, the extra explanation can make first time exposure much easier for people like myself.
Amazing videos I am thinking on completing all of your videos on Calculus 1 and 2!
Now i can feel physics equations Reason-You
Just loved the beauty of mathematics. How Awesome these concepts can be applied in physics
❤wow.. It's very interesting concept.. Our great coach❤😊 . .. From INDIA🇮🇳
I'd like to see a derivation of the derivative involving a ratio of two directed integrals as expressed in the Geometric Calculus of Dr. David Hestenes.
Hello there professor long time no see!!!
So I know to find instantaneous velocity I can get it by using ds/dt
where the rise / run are really small
and as I know velocity is a function dependable on time we can tell what is the velocity of the object at a specific time but I stumbled a video in related rates which my school teacher sent me and the guy in the video said " dr / dt , where dr is the change of radius in an inflating balloon , when r = 4 " , now this time the guy didn't say it at a specific time but rather said at a specific radius now , when he said that did he mean small change such as f(4+dt)-4 /dt ?If not please help me visualise it professor! THANKS!!!!
When he said r = 4 he meant it at a specific time :D , Thanks for replying :)
Thank you so much! I thought I was dump before i find out that my teachers are awful