Exam 3: Differentiation Rules

Let be the total value of US currency (coins and banknotes) in circulation at time.The table gives values of this function from 1980 to 2000, as of September 30, in billions of dollars.Estimate the value of C Select the correct Answer Answers are in billions of dollars per year.Round yourAnswer to two decimal places.

Select the correct Answer for each question. -Use implicit differentiation to find an equation of the tangent line to the curve at the indicated point.

has a half-life of days.A sample has a mass of mg initially.Find a formula for the mass remaining after days.

Select the correct Answer: for each question. -Use the definitions of the hyperbolic functions to find the following limit.

Select the correct Answer for each question. -The equation of motion is given for a particle, where is in meters and is in seconds.Find the acceleration after seconds.

Find the average rate of change of the area of a circle with respect to its radius as changes from to Select the correct Answer

Find the value of the expression accurate to four decimal places.

Calculate

Find the point(s) on the graph of where the tangent line is horizontal.

Find the equation of the tangent line to the given curve at the specified point.

Find

The volume of a right circular cone of radius and height is Suppose that the radius and height of the cone are changing with respect to time a.Find a relationship between b.At a certain instant of time, the radius and height of the cone are 12 in.and 13 in.and are increasing at the rate of 0.2 in./sec and 0.5 in./sec, respectively.How fast is the volume of the cone increasing?

Find the derivative of the function.

Differentiate.

A 18-ft ladder leaning against a wall begins to sl ide.How fast is the angle between the ladder and the wall changing at the instant of time when the bottom of the ladder is 9 ft from the wall and sliding away from the wall at the rate of 4 ft/sec? Round theAnswer to the nearest hundredth.

Find the derivative of the function.

Select the correct Answer for each question. -Differentiate:

Select the correct Answer for each question. -Use the definition of the derivative to find the derivative of the function.

Find the derivative of the function.Select the correct Answer

Calculate