A minimization fencing problem.

A rectangular field is going to be enclosed and divided into two separate rectangular areas. (Areas do not have to be equal). Find the minimum fencing that is required if the total area of the field is 1200m2.

Maximization

Find two real numbers whose sum is 10 and whose product is maximal?

Volume of solids of revolution: two methods

Find the volume of the solid generated when the region bounded by y = sqrRoot(x-1); y = 0 and x = 5 is rotated about the line y = 3. Use both methods, washer (disk) and shell, showing that both methods yield the same answer.

How do I know when to use the Chain Rule and when not to?

The question is answered by contrasting the procedures for taking the derivatives of f(x)=x^2-3x+7 and f(x)=(x^2-3x+7)^4.

Help me to understand the formal setup of the Chain Rule.

The procedure is shown using the easy example y=(5x^4+3x^2-2)^7.

Chain rule

Use Chain rule to solve: y=sin((ln(x^2+e^x)+2)^(1/2))^3.

Trigonometric Functions and Trigonometric Identities

I need to know the trigonometric functions and trigonometric identities.

Definition of derivative

Let f(x) be a continuous function of one variable. a) Give the definition of the derivative. b) Use this definition to find the derivative of f(x)=x^2+2x-5 c) Evaluate f'(2)

Limit

Explain the purpose of a limit using the function (x^2-4)/(x-2).

Calculus

1. A weather balloon is rising vertically at a constant rate of 4 ft/s directly above a straight and level road. When the balloon is 75 ft above the road, a car moving at 55 ft/s passes directly under the balloon. Based on this information find: a. the rate the distance between the balloon and the car is changing 3 sec after t ...continues