Slope Fields
Flashcard
•
Mathematics
•
10th Grade - University
•
Practice Problem
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a slope field?
Back
A slope field is a graphical representation of the solutions to a first-order differential equation, showing the slopes of the solution curves at various points in the plane.
Tags
CCSS.8.EE.C.8B
2.
FLASHCARD QUESTION
Front
How do you interpret the slopes in a slope field?
Back
The slopes in a slope field indicate the direction of the solution curves at each point. The steeper the slope, the faster the function is changing at that point.
3.
FLASHCARD QUESTION
Front
What does dy/dx represent in the context of slope fields?
Back
In slope fields, dy/dx represents the derivative of y with respect to x, indicating the slope of the tangent line to the solution curve at a given point.
Tags
CCSS.HSA-REI.B.4B
4.
FLASHCARD QUESTION
Front
What is the significance of the equation dy/dx = sin x in a slope field?
Back
The equation dy/dx = sin x indicates that the slope of the solution curve varies with the sine of x, leading to periodic behavior in the solutions.
5.
FLASHCARD QUESTION
Front
How can you determine the slope field for dy/dx = -x/y?
Back
To determine the slope field for dy/dx = -x/y, you would plot slopes at various points (x, y) based on the negative ratio of x to y.
6.
FLASHCARD QUESTION
Front
What is the general form of a first-order differential equation?
Back
The general form of a first-order differential equation is dy/dx = f(x, y), where f is a function of x and y.
7.
FLASHCARD QUESTION
Front
What does the slope field look like for dy/dx = 1/2x + 1?
Back
The slope field for dy/dx = 1/2x + 1 will show slopes that increase linearly with x, indicating a linear relationship between the slope and the x-coordinate.
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