How do you draw slope fields?
Example:
How do you draw the slope field for
The slope field is a cartesian grid where you draw lines in various directions to represent the slopes of the tangents to the solution. Therefore by drawing a curve through consecutive slope lines, you can find a solution to the differential equation.
Take the example of
#dy/dx = 3  4 =1#
So you would draw a line of slope
Hopefully this helps!
By signing up, you agree to our Terms of Service and Privacy Policy
To draw a slope field:

Choose a grid: Draw a grid on a coordinate plane. The grid should cover the region of interest and have equally spaced horizontal and vertical lines.

Determine the differential equation: Given a firstorder ordinary differential equation (ODE) of the form dy/dx = f(x, y), identify the function f(x, y).

Calculate slopes: For each point (x, y) in the grid, calculate the slope at that point using the function f(x, y). This involves evaluating f(x, y) at each point to find the slope.

Draw arrows: At each point on the grid, draw a short line segment or arrow with the calculated slope. The direction of the arrow indicates the direction of the slope, and the length of the arrow represents the magnitude of the slope.

Refine the slope field: Adjust the density of arrows as needed to accurately represent the behavior of the solution curves. You may need to add more arrows in regions with rapidly changing slopes or fewer arrows in regions with relatively constant slopes.

Optional: Add solution curves: If you have specific initial conditions for the ODE, you can sketch solution curves on the slope field by following the direction indicated by the arrows.

Label axes and add titles: Finally, label the x and y axes and add any necessary titles or labels to the slope field to provide context for the graph.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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 onesided 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 onesided 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 onesided 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.
 How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the yaxis given #y=16xx^2#, x=0, and y=64?
 How do you find the general solution to #dy/dx=1/sec^2y#?
 How to find the auxillary equation and the final solution for #(d^2Phi)/(dphi^2) + BPhi = 0# assuming #Phi = e^(im_lphi)#?
 What is the arclength of #f(x)=(x2)/(x^2x2)# on #x in [1,2]#?
 How do you find the volume of the solid obtained by rotating the region bounded by the curves #y=x^2# and #y=2x^2# and #x=0# about the line #x=1#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7