A cube is growing in size. What is the ratio of the rate of growth of the cube's surface area to the rate of growth of its diagonal when its sides have length ?

Compute the differential for the following.

Using the method of midpoint Reimann sums, approximate the integral using three midpoints.

A spherical balloon is being filled with air. What is the volume of the sphere at the instance the rate of growth of the volume is times the rate of growth of the surface area?

A cube is growing in size. What is the ratio of the rate of growth of the cube's volume to the rate of growth of its surface area when its sides have length ?

A trapezoid is changing in shape. The parallel sides have lengths and , and the height is . If the short and long sides are growing at a rate of and , and the height is constant, what is the rate of growth of the area?

Let on the interval . How many values of x exist that satisfy the mean value theorem for this function and interval?

Using the method of midpoint Reimann sums, approximate the integral of the function over the interval using four midpoints.

Utilize the method of midpoint Riemann sums to approximate using three midpoints.

A cube is growing in size. What is the length of the diagonal of the cube at the time that the rate of growth of the cube's surface area is equal to 32 times the rate of growth of its diagonal?