A spherical balloon is being filled with air. What is ratio of the rate of growth of the surface area of the sphere to the rate of growth of the circumference when the radius is 160?

A regular tetrahedron is growing in size. What is the ratio of the rate of change of the volume of the tetrahedron to the rate of change of its surface area when its sides have length 1.8?

Consider the function between and . Find the definite integral using midpoint Riemann sums with two rectangles.

A spherical balloon is deflating, although it retains a spherical shape. What is ratio of the rate of loss of the volume of the sphere to the rate of loss of the radius when the radius is 17?

Find for the function below:

Hint: Use implicit differentiation.

A cube is growing in size. What is the length of the sides of the cube at the time that the rate of growth of the cube's volume is equal to 0.56 times the rate of growth of its surface area?

Let on the interval . Find a value for the number that satisfies the mean value theorem for this function and interval.

The velocity of an errant particle is given by the function . Approximate the average velocity of the particle over the interval of time using the method of midpoint Reimann sums and four midpoints.

Find for the function below:

Hint: Use implicit differentiation.

A regular tetrahedron is burgeoning in size. What is the ratio of the rate of change of the surface area of the tetrahedron to the rate of change of its height when its sides have length 17?