Exam 2: Functions, Limits and the Derivative

At a temperature of , the volume V (in liters) of 1.33 g of is related to its pressure p (in atmospheres) by the formula . What is the average rate of change of V with respect to p as p increases from to ? What is the rate of change of V with respect to p when

A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $15,000, and the variable cost for producing x pagers/week is dollars. The company realizes a revenue of dollars from the sale of x pagers/week. What is the profit for the company if 2,000 units are produced and sold each week?

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

Find the values of x for which the function is continuous.

Determine all values of x at which the function is discontinuous.

Use the intermediate value theorem to find the value of c such that . __________

Under a set of controlled laboratory conditions, the size of the population of a certain bacteria culture at time t (in minutes) is described by the function Find the rate of the population growth at t = 30 min.

The owner of a luxury motor yacht that sails among the 4,000 Greek islands charges $800/person/day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up (up to the maximum capacity of 90) for the cruise, then each fare is reduced by $4 for each additional passenger. Assume at least 20 people sign up for the cruise and let x denote the number of passengers above 20. Find a function R giving the revenue/day realized from the charter.

Find the limit, if it exists. Otherwise, answer no solution.

Use the graph of the given function f to determine at the indicated value of a. __________

Find the limit.

Find the limit, if it exists.

Find function f such that and

Determine whether the given function is a polynomial function or rational function. State the degree, if it is polynomial function. Answer polynomial or rational. __________ If a polynomial function, the degree is __________

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. X = 5y - 25

Find the values of x for which the function is continuous.

The revenue (in dollars) realized by Apollo from the sale of its inkjet printers is given by where x denotes the number of units manufactured each month. What is Apollo's revenue when 2,000 units are produced? $__________

The revenue (in dollars) realized by Apollo from the sale of its inkjet printers is given by where x denotes the number of units manufactured each month. What is Apollo's revenue when 1,500 units are produced?

Determine all values of x at which the function is discontinuous.