How do you sketch a slope field for #dy/dx = (x + 1)^2/y#?

Answer 1

The slope field is pretty much a bunch of lines that represent the slopes of the solution points. For instance, if we have the point #(0, 2)# is a solution to the differential equation above, you should find that the slope on the field should be #(0 + 1)^2/2 = 1/2#,

Here is the slope field for the given differential equation. The black curve would be one particular solution to the equation. A solution is given by following the slopes.

Hopefully this helps!

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Answer 2

To sketch a slope field for the differential equation dy/dx = (x + 1)^2 / y, follow these steps:

  1. Choose a range for x and y values over which you want to sketch the slope field.
  2. Divide this range into a grid of points (x, y).
  3. At each grid point (x, y), calculate the slope dy/dx using the given equation.
  4. Draw a short line segment with the calculated slope at each grid point.
  5. Repeat steps 3 and 4 for all grid points to create the slope field.

This slope field represents the direction of the solution curves for the given differential equation at different points in the x-y plane.

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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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