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Campbell University

University of Michigan - Ann Arbor

Idaho State University

Boston College

00:51

Heather Zimmers

If $f(x)=x+\sqrt{2-x}$ and $g(u)=u+\sqrt{2-u},$ is it true that $f=g ?$

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Virendrasingh Deepaksingh

01:09

Felicia Sanders

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So now that we're very familiar with what a vector is and kind of the ways we can combine vectors and use vectors to describe different types of objects, we want to talk about factor valued functions. And so the benefits of victor value functions is we saw At the end of the last lecture are set of lectures that vectors can be used to describe planes and lines. But we actually want to use vectors to describe more than just planes and lines, but really arbitrary curves. So vector value functions. We're going to give us a way to actually describe Let's say, I just have some random curve and now this curve might represent, like the position of a particle particle moving through space. So vector value functions air gonna allow us to mathematically described curbs like this. And then what we're going to see is that we can actually do calculus with these vector valued functions and in the back of the mind, well of our mind will always think about this particle moving. And so when we do the calculus of these vector value functions, we're gonna see that we can actually find the velocity of this particle as it moves and the acceleration and how is it changing and its speed and all these different things, you know? So beyond that, we are going to talk a little bit about the motion of particles using these vector value functions. Another thing we'll talk about is links of these curves that we can describe with victor value functions, and this is going to be really important. It may seem like a sort of a tangent, but when we do what's called line in a girl's later in the course, it's really just going to come down to this method of finding the length of a curve where were sort of gonna wait it within what's called a vector field. Eso this really is going to be a key player later this idea of how we find the length of a curve on, but it's also of its own interest. It also represents, you know, going back toe. If this is the motion of a particle, well, it's also gonna basically tell us how far the particle traveled. You know what is the distance along this curve that this particle is moving

Functions of Several Variables

Partial Derivatives

Multivariable Optimization

Multiple Integrals

Vector Calculus

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07:30

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03:11

15:41

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02:47

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10:06

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