Question

Hey can someone please explain to me how to figure out how to match slope fields to their graphs without the use of a calculator? for problem such as these: y'=-y b) y'=x-y c) y'=1/y

Answer 1

It really depends on how the give choice are look like.
We can always try to extract some special feature of each equatio.
For example for \(y]=-y\) we know that when \(y=0\) we have \(y'=0\). So along the x-axis the slope fields are horizontal line segments. But it is possible that the other graph has this feature. Then for example you look at \(y=1\). Here \(y'=-1\). So along the line \(y=1\) the slopes are all -1 and so on...

Answer 2

no my question is how do you test for conditional convergence and absolute convergence

Answer 3

please ignore the previous comment . so we plug zero in for y' zero

Answer 4

can you please explain how to do it for y'=1/y

Answer 5

for y'=1/y for example we can see that for y=0 the slope is undefined. So along the x-axis there is no slope field

Answer 6

so we plug zero in for y ?

Answer 7

yes, but 1/0 is undefined.

Answer 8

but what i dont understand is my teacher wrote on the board for this problem y=0 y>0 y'= undefined y'>0 do you know how she came up with the inequality part

Answer 9

I think what your techer meant was y' is undefined for y=0. And y' >0 for y>0

Answer 10

do you know how she came up with that

Answer 11

well, if y>0, then 1/y >0. Since y'=1/y. Then y' >0 too.

Answer 12

so you have to look at each quadrant on the graph to figure it out

Answer 13

Since this is about matching as I said earlier it depends on the given choices. Maybe by just analyzing for y>0 it is enough to see the the behavior of the right graph. If it is not enough my by you need an analysis for y<0. But basically you just plug in some certain values of y (or x) so that you can see a property that the right graph has but the others are not.

Answer 14

okay . how would you do it for y'=x

Answer 15

would you say x=0 and y'=0

Answer 16

yes, for x=0 we have y'=0. But the other slope field might be has this feature too. So you need to look at for something else in that case. Say plug in x=1 to get y'=1. If the other slope field also have this feature then you need to look at for something else... and so on....

Answer 17

so on the y axis you have horizontal lines got through it

Answer 18

correct!

Answer 19

i wanted to check with you one more so if you y'=4-y . you plugin zero for y an you get y=0 , y'=-4

Answer 20

yes, but maybe the slope of -4 is not very easy to see. So instead plug in y=4 to get y'=0.

Answer 21

okay i see so you can plug in whatever you want

Answer 22

correct! :)

Answer 23

also, if you want to check based on quadrants so the for example you explained to me y'=y
you could say when y>0 ,y'> 0

Answer 24

yes, you can do that as well :).

Answer 25

hey do you think i can ask you another question because you have been very helpful

Answer 26

hey do you think i can ask you another question because you have been very helpful