Question

The differential equation dy/dx = (x+1)/(x-2)

Answer 1

The differential equation \[\frac{ dy }{ dx } = \frac{ x+1 }{ x-2 }\]

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

I only
II only
I and II only
all of them
II and III only

Answer 2

I. No. It's at x = +1
II. Yes. x = 2 makes the denominator explode.
III. You tell me.

Answer 3

i would assume that III is correct, because is vertical tangents, wouldnt it be parallel?

Answer 4

?? Not sure that makes any sense.

Answer 5

actually mb, its not parallel because tangents arent straight lines are they?

Answer 6

?? You seem to be struggling with exactly what a Slope Field is.

As we get away from x = 0, far away, the slope tends toward +1

At x = -1, we have 0/(-3) = 0. So actually, I is good. It is tangents are horizontal for x= -1. You should have argued with me on that point.