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Relative change in blood velocity Suppose $y=f(x)$ and $x$ and $y$ change by amounts $\Delta x$ and $\Delta y .$ A way of expressing a linear approximation is to write $\Delta y \approx f^{\prime}(x) \Delta x$ The relative change in $y$ is $\Delta y / y$ .A special case of Poiseuille's law of laminar flow (see Example 3.3 .9 ) is that at the central axis of a blood vessel the velocity of the blood is related to the radius $R$ of the vessel by an equation of the form $v=c R^{2} .$ If the radius changes, how is the relative change in the blood velocity related to the relative change in the radius? If the radius is increased by $10 \%,$ what happens to the velocity?
the velocity increases by $20 \%,$ if radius is increased by 10$\% .$
Calculus 1 / AB
Chapter 3
Derivatives
Section 8
Linear Approximations and Taylor Polynomials
Harvey Mudd College
Baylor University
University of Michigan - Ann Arbor
University of Nottingham
Lectures
03:09
In mathematics, precalculu…
31:55
In mathematics, a function…
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The velocity $ v $ of bloo…
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Blood flow The velocity $v…
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Blood Flow As blood moves …
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Blood flow In Example 3.3 …
00:45
Relative change in blood f…
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Refer to the law of lamina…
01:24
Poiseuille's Law Unde…
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Let $v(r)$ be the velocity…
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When blood flows along a b…
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Blood flow The shape of a …
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As blood moves through a v…
01:59
When blood flows through a…
00:48
The velocity $(\mathrm{in}…
02:12
Poiseuille's Law Acco…
03:39
Blood Flow In an example f…
01:06
07:00
Blood Flow The figure show…
02:46
01:43
(II) Poiseuille's equ…
in this problem. It decided that if we have a function, why which is fo pecs and increments off about the X and Uncle Mark, then the approximation to be changing Why is that? Primal backs of charitable function must abide by the change in X step. And there lt Gen. Gen y is equal to a final banks. That's extra wide by what? So we've given that to function Why or effort guys is the And these he concludes si r squared. So from this first, let's find the marital dysfunction like perm which respect to our that would be to see. So I just took to their patrol this function. So that is equal to okay, that is their reproductive function. So we need to find the change in the okay which is a prime of X d s. What is that primal? It's well, we just found it does see our square. What is the x in this problem are these are X and he is our war sword on D X would be D r a minimum stage. That should be to see. So then change your wife is to see our What is the role to change. Why or V or philosophy. It is to see our delta are derided by the what is we just see our squared. So then, from this religion, change in velocity is two times your love. You're changing radio's Okay, So from this, if be radius um increases by 10% then the velocity should increase by 20%.
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