Question

A particle moves in a velocity field $\mathbf{V}(x, y)=\left\langle x^2, x+y^2\right\rangle$. If it is at position $(2,1)$ at time $t=3$, estimate its location at time $t=3.01$.

   A particle moves in a velocity field $\mathbf{V}(x, y)=\left\langle x^2, x+y^2\right\rangle$. If it is at position $(2,1)$ at time $t=3$, estimate its location at time $t=3.01$.
 
Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
James Stewart,… 9th Edition
Chapter 16, Problem 37 ↓
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A particle moves in a velocity field $\mathbf{V}(x, y)=\left\langle x^2, x+y^2\right\rangle$. If it is at position $(2,1)$ at time $t=3$, estimate its location at time $t=3.01$.
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Transcript

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00:01 Today we're going to consider a particle in the velocity vector field x squared x plus y squared now at time equals three the particle is at the point two one and we're going to estimate where it will be at time 3 .01 now we're just going to use speed which can call v or velocity is distance over time so the change in time is 3 .01 minus 3 .01 and 3 .3 this is 0 .01.
00:39 Our velocity at this point is we plug in to 1, which when we plug in 2, we'll get 4, and then we'll have 2 plus 1, which is 3.
00:56 And then the distance is our time, or our change in time, times our velocity at that point.
01:10 And our changing time is 0 .0 .1, and our last year's 4 .3...
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