How do you draw the slope field of the differential equation #y'=(y^2-y-2)(1-y^2)# ?

Answer 1

See below.

In red the equilibrium points.

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Answer 2

To draw the slope field of the differential equation ( y' = (y^2 - y - 2)(1 - y^2) ), you follow these steps:

  1. Choose a set of ( x ) and ( y ) values to plot in the ( xy )-plane.
  2. For each ( (x, y) ) point, calculate the value of ( y' ) using the given differential equation.
  3. Plot a small line segment with slope equal to the calculated value of ( y' ) at each ( (x, y) ) point.

Repeat these steps for various ( x ) and ( y ) values to obtain a visual representation of the slope field across the ( xy )-plane.

Keep in mind that the slope field provides a visual guide to the behavior of solutions to the differential equation. It illustrates how the slope of the solution curve changes at different points in the ( xy )-plane based on the given differential equation.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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