Flashcard over writing equations with finite differences

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a finite difference?
Back
A finite difference is a mathematical expression of the form f(x + h) - f(x), where h is a small increment. It is used to approximate derivatives and analyze sequences.
2.
FLASHCARD QUESTION
Front
What does the first finite difference represent?
Back
The first finite difference represents the change in the values of a function as the input changes, indicating the slope or rate of change.
3.
FLASHCARD QUESTION
Front
What does the second finite difference indicate?
Back
The second finite difference indicates the rate of change of the first finite difference, which helps determine the curvature of the function.
4.
FLASHCARD QUESTION
Front
How can you determine if a function is linear using finite differences?
Back
If the first finite difference is constant, the function is linear.
5.
FLASHCARD QUESTION
Front
How can you determine if a function is quadratic using finite differences?
Back
If the second finite difference is constant, the function is quadratic.
6.
FLASHCARD QUESTION
Front
What is the general form of a linear equation?
Back
A linear equation can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.
7.
FLASHCARD QUESTION
Front
What is the general form of a quadratic equation?
Back
A quadratic equation can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.
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