anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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watchmath
  • watchmath
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...
anonymous
  • anonymous
no my question is how do you test for conditional convergence and absolute convergence
anonymous
  • anonymous
please ignore the previous comment . so we plug zero in for y' zero

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anonymous
  • anonymous
can you please explain how to do it for y'=1/y
watchmath
  • watchmath
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
anonymous
  • anonymous
so we plug zero in for y ?
watchmath
  • watchmath
yes, but 1/0 is undefined.
anonymous
  • anonymous
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
watchmath
  • watchmath
I think what your techer meant was y' is undefined for y=0. And y' >0 for y>0
anonymous
  • anonymous
do you know how she came up with that
watchmath
  • watchmath
well, if y>0, then 1/y >0. Since y'=1/y. Then y' >0 too.
anonymous
  • anonymous
so you have to look at each quadrant on the graph to figure it out
watchmath
  • watchmath
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.
anonymous
  • anonymous
okay . how would you do it for y'=x
anonymous
  • anonymous
would you say x=0 and y'=0
watchmath
  • watchmath
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....
anonymous
  • anonymous
so on the y axis you have horizontal lines got through it
watchmath
  • watchmath
correct!
anonymous
  • anonymous
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
watchmath
  • watchmath
yes, but maybe the slope of -4 is not very easy to see. So instead plug in y=4 to get y'=0.
anonymous
  • anonymous
okay i see so you can plug in whatever you want
watchmath
  • watchmath
correct! :)
anonymous
  • anonymous
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
watchmath
  • watchmath
yes, you can do that as well :).
anonymous
  • anonymous
hey do you think i can ask you another question because you have been very helpful
anonymous
  • anonymous
hey do you think i can ask you another question because you have been very helpful

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