It's the second day of school and I just got switched into an ap calculus class. I went to the teacher and asked about what I missed, he gave me a worksheet and told me it was due tomorrow. I am way out of my depth and up until today, I had never heard of an instantaneous rate of change. this video was extremely helpful.
Incorporating visuals while learning is so much more efficient I really want to thank you for taking the time to make these really helping me conceptualize the theorys of these formulas with calculus
I've seen many videos about why there is something called limit including your next video, but this is the only video showed me the value of limit!!! Great Job
What use is the instantaneous rate of change, what can i do with it ?. lets say i calculate my answer as 2, what now, what does 2 tell me, what do i do with it ? 2 cpmpared to what or what does 2 correspond to ?
Quick question. If I'm told to estimate the instataneous rate of change of each function at the given point. f(x)=x^3+x^2 (2,12) . Would I do f(2.01)-f(1.99)/2.01-1.99 ? I saw that you used the point and used the other point closer which one is correct?
I don't understand what is the point of continuously moving the second point closer and closer. Why not just start with the second point being really close to begin with?
you can do that. this is just an introduction video for instantaneous rate of change and showing where the concept comes from. a more efficient way to do this is using derivatives.
Hi James.. I agree with u..in my class v tried getting a reallly really close point ; a point where d calculations drive u crazy but the esmitated avg. remains d same !
I cannot understand the idea of instantaneous rate of change. How it is possible for change to exist at a single point? When something changes it changes with respect to some previous point? So how it is possible to attribute rate of change to a single point?
I could use some help.. I can't remember the name of how to get the slope formula of a formula, and google can't seem to help. X^2 --> 2X X^3+5 --> 3X^2+0 Does anyone know what this is called?
By watching the animation speaking completely out of tune with the narrator voice over, I'm reminded of the old kung fu movies of the 70's and late 60's. LOL.... But a great and easy to understand explanation of the "instantaneous rate of change", I must add!
Convincing but not scientific.Newton derived exact value of derivative,without limits from his method of fluxions.Due to intellectual poverty ,all others misunderstood this dubius limits which is unscientific by several examples.
Hi Steven. PowToon is the software I use to make these animations. It's a lot like using PowerPoint. You just load up the voice over and set the timing of when things will appear and disappear. Check it out: www.powtoon.com/home/?
They do have a free version. The restrictions are: 100MB file size, "PowToon" branding, limited picture libraries. Here is the details some of the paid options: www.powtoon.com/pricing/edu/ Feel free to send me an e-mail and I can help you out a bit more. I'm a teacher too, and I know how tough it can be finding good free tools for lessons. :^D
These videos are seriously helping me. I'm a 36 year old engineering student who thought I had math confidence and I survived trigonometry but calculus is so conceptual and it has really made me feel lost and dumb despite it looking so simple. These really help to clear it all up.
Why don't we just draw a tangent of a point on a curve and calculate its gradient? Wouldn't it give the exact value of the rate of change at that particular point?
