AP Calculus Unit 4 Review
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the formula for the volume of a sphere?
Back
V = \frac{4}{3} \pi r^3
Tags
CCSS.8.G.C.9
CCSS.HSG.GMD.A.3
2.
FLASHCARD QUESTION
Front
How do you find the rate of change of volume with respect to time for a spherical balloon?
Back
Use the formula \frac{dV}{dt} = \frac{dV}{dr} \cdot \frac{dr}{dt} and apply the chain rule.
3.
FLASHCARD QUESTION
Front
What is the derivative of the volume of a sphere with respect to its radius?
Back
\frac{dV}{dr} = 4\pi r^2
4.
FLASHCARD QUESTION
Front
If the radius of a spherical balloon is decreasing, how does it affect the volume?
Back
The volume decreases as the radius decreases.
5.
FLASHCARD QUESTION
Front
What is the relationship between position, velocity, and acceleration in calculus?
Back
Acceleration is the derivative of velocity, and velocity is the derivative of position.
6.
FLASHCARD QUESTION
Front
How do you find the acceleration of an object given its position function?
Back
Take the second derivative of the position function with respect to time.
7.
FLASHCARD QUESTION
Front
What is linear approximation in calculus?
Back
Linear approximation uses the tangent line at a point to estimate the value of a function near that point.
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