Related Rates

Front

What is the formula for the volume of a cube?

Back

V = s³, where s is the length of an edge of the cube.

Front

How do you find the rate of change of the area of a circle when given the rate of change of its circumference?

Back

Use the relationship A = πr² and the fact that C = 2πr. Differentiate both with respect to time.

Front

What is the relationship between the circumference of a circle and its radius?

Back

C = 2πr, where C is the circumference and r is the radius.

Front

What is the formula for the Pythagorean theorem?

Back

a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse.

Front

How do you determine the rate of change of distance between an observer and a moving object?

Back

Use related rates and differentiate the distance formula with respect to time.

Front

What is the formula for the area of a circle?

Back

A = πr², where A is the area and r is the radius.

Front

What is the significance of related rates in calculus?

Back

Related rates problems involve finding the rate at which one quantity changes in relation to another.

Front

How do you apply the chain rule in related rates problems?

Back

Use the chain rule to differentiate composite functions that relate different quantities.

Front

What is the formula for the derivative of the area of a circle with respect to time?

Back

dA/dt = (dA/dr) * (dr/dt) = 2πr * (dr/dt).

Front

What is the relationship between the radius and the area of a circle?

Back

The area increases with the square of the radius, A = πr².