Slope Fields

• 10 1 Slope Field Sap Calculus Calculator
• 10 1 Slope Field Sap Calculus Formula
• 10 1 Slope Field Sap Calculus Formulas
• 10 1 Slope Field Sap Calculus Equation

10 1 Slope Field Sap Calculus Calculator

10 1 Slope Field Sap Calculus Formula

From the May 2008 AP Calculus Course Description: 15. The slope field from a certain differential equation is shown above. Which of the following could be a specific solution to that differential equation? (A) yx= 2 (B) ye= x (C) ye= −x (D) yx=cos (E) yx=ln 16. The slope field for a certain differential equation is shown above. So at this point your slope negative one one so negative negative one is one over one, so you're going to have a slope like that. At negative two two same exact idea, it would look like that. And so when you keep drawing these line segments over these kind of sample points in the cartesian or in the x-y plane, you start to get a sense of well. Slope fields are little lines on a coordinate system graph that represent the slope for that (x,y) combination for a particular differential equation (remember that a differential equation represents a slope).

Need calculus help? Ask your own question. This is how you slader. Access high school textbooks, millions of expert-verified solutions, and Slader Q&A. If we want to find the slope of the line tangent to the graph of at the point, we could evaluate the derivative of the function at. On the other hand, if we want the slope of the tangent line at the point, we could use the derivative of. However, it is not always easy to solve for a function defined implicitly by an equation.

10 1 Slope Field Sap Calculus Formulas

Key Questions

10 1 Slope Field Sap Calculus Equation

• Example:

  How do you draw the slope field for #dy/dx = x - y#?

  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# at #(3, 4)#. Here we see that

  #dy/dx = 3 - 4 =-1#

  So you would draw a line of slope #-1# at #(3,4)#. Repeat this for maybe 4 by 4 points to get the following slope field

  Hopefully this helps!

• If you are allowed to use a software, then a software called GeoGebra gives us the slope field below.

  I hope that this was helpful.

• Slope field can be used to visualize the flow of the solution curves of its corresponding differential equation. At each point of the solution curve, the curve will have the slope indicated in the slope field.

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