Question

Match the vector fields $\mathbf{F}$ with the plots labeled I-VI. Give reasons for your choices. $\mathbf{F}(x, y)=\langle x,-y\rangle$ Figure I-VI can't copy 

   Match the vector fields $\mathbf{F}$ with the plots labeled I-VI. Give reasons for your choices.
$\mathbf{F}(x, y)=\langle x,-y\rangle$

Figure I-VI can't copy
Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
James Stewart,… 9th Edition
Chapter 16, Problem 13 ↓
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Match the vector fields $\mathbf{F}$ with the plots labeled I-VI. Give reasons for your choices. $\mathbf{F}(x, y)=\langle x,-y\rangle$ Figure I-VI can't copy
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Match the vector fields $\mathbf{F}$ with the plots labeled I-VI. Give reasons for your choices. $\mathbf{F}(x, y)=\langle y, x-y\rangle$

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Match the vector fields $F$ with the plots labeled I-IV. Give reasons for your choices. $$ \mathbf{F}(x, y)=\langle y, y+2\rangle $$
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Transcript

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00:01 So we have an expression here, we'd like to match it to its vector field.
00:04 And how can we do this? well, the x component is just y.
00:09 So if we look at this, we expect in general, whenever y is positive, we're going to the right.
00:17 And whenever y is negative, we're going to the left.
00:23 So that's good.
00:24 And for the y component, we're going up whenever x is greater than y, and down whenever x is less than y.
00:36 So that's good and cool.
00:38 Let's see what we can get here...
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