Questions from General Calculus

Q: In this section we discussed examples of ordinary, everyday functions:

In this section we discussed examples of ordinary, everyday functions: Population is a function of time, postage cost is a function of weight, water temperature is a function of time. Give three other...

Q: Find a formula for the described function and state its domain.

Find a formula for the described function and state its domain. A closed rectangular box with volume 8 ft3 has length twice the width. Express the height of the box as a function of the width.

Q: Find a formula for the described function and state its domain.

Find a formula for the described function and state its domain. An open rectangular box with volume 2m3 has a square base. Express the surface area of the box as a function of the length of a side of...

Q: A Norman window has the shape of a rectangle surmounted by a

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 30 ft, express the area A of the window as a function of the width x of the window.

Q: A box with an open top is to be constructed from a

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides a...

Q: A cell phone plan has a basic charge of $35 a

A cell phone plan has a basic charge of $35 a month. The plan includes 400 free minutes and charges 10 cents for each additional minute of usage. Write the monthly cost C as a function of the number x...

Q: In a certain state the maximum speed permitted on freeways is 65

In a certain state the maximum speed permitted on freeways is 65 mi/h and the minimum speed is 40 mi/h. The fine for violating these limits is $15 for every mile per hour above the maximum speed or be...

Q: An electricity company charges its customers a base rate of $10

An electricity company charges its customers a base rate of $10 a month, plus 6 cents per kilowatt­hour (kWh) for the first 1200 kWh and 7 cents per kWh for all usage over 1200 kWh. Express the monthl...

Q: In a certain country, income tax is assessed as follows.

In a certain country, income tax is assessed as follows. There is no tax on income up to $10,000. Any income over $10,000 is taxed at a rate of 10%, up to an income of $20,000. Any income over $20,000...

Q: The functions in Example 10 and Exercise 67 are called step functions

The functions in Example 10 and Exercise 67 are called step functions because their graphs look like stairs. Give two other examples of step functions that arise in everyday life.