AP Calculus Unit 4 Review

Front

What is the formula for the volume of a rectangular prism?

Back

The volume V of a rectangular prism is given by V = length × width × height.

Tags

CCSS.7.G.B.6

Front

How do you find the rate of change of the water level in a rectangular pool?

Back

To find the rate of change of the water level, use the formula: rate = volume flow rate / (length × width).

Front

What is linear approximation in calculus?

Back

Linear approximation is a method of estimating the value of a function near a given point using the tangent line at that point.

Front

What is the derivative of f(x) = x^3 - x?

Back

The derivative f'(x) = 3x^2 - 1.

Front

What is the limit of a function?

Back

The limit of a function is the value that the function approaches as the input approaches a certain point.

Front

How do you evaluate limits involving trigonometric functions?

Back

Use trigonometric identities and algebraic manipulation to simplify the expression before applying limit laws.

Front

What is the formula for the volume of a cone?

Back

The volume V of a cone is given by V = (1/3)πr^2h, where r is the radius and h is the height.

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

Front

How do you find the rate of change of the water level in a cone-shaped container?

Back

Use the formula: rate = volume flow rate / (1/3)πr^2h, adjusting for the relationship between r and h.

Front

What is acceleration in terms of position function?

Back

Acceleration is the second derivative of the position function with respect to time, a(t) = d²x/dt².

Front

How do you find the acceleration of an object given its position function?

Back

Differentiate the position function twice with respect to time to find the acceleration.