Asked by Alice
The differential equation dy/dx=(x+1)/(x-2)
I. produces a slope field with horizontal tangents at x = −1
II. produces a slope field with vertical tangents at x = 2
III.produces a slope field with rows of parallel segments
a) I and II only
b) II only
c) III only
d) I only
I. produces a slope field with horizontal tangents at x = −1
II. produces a slope field with vertical tangents at x = 2
III.produces a slope field with rows of parallel segments
a) I and II only
b) II only
c) III only
d) I only
Answers
Answered by
oobleck
clearly, for any constant value of x, dy/dx is constant.
since x-2=0 when x=2, the slope field is vertical there
to get rows of parallel segments, you need a constant value for y. But that means you need (x+1) = y(x-2), which has only one solution. SO, no rows of parallel segments.
Looks like I and II only, right?
You know, there are online sites for checking slope fields. One of them is
https://www.desmos.com/calculator/p7vd3cdmei
Just change the function and watch the screen.
since x-2=0 when x=2, the slope field is vertical there
to get rows of parallel segments, you need a constant value for y. But that means you need (x+1) = y(x-2), which has only one solution. SO, no rows of parallel segments.
Looks like I and II only, right?
You know, there are online sites for checking slope fields. One of them is
https://www.desmos.com/calculator/p7vd3cdmei
Just change the function and watch the screen.
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