Questions from General Calculus

Q: Find two positive numbers, x and y, whose sum is

Find two positive numbers, x and y, whose sum is 100 and whose product is as large as possible.

Q: Find two positive numbers, x and y, whose product is

Find two positive numbers, x and y, whose product is 100 and whose sum is as small as possible.

Q: Find the equation of the tangent line to the curve y =

Find the equation of the tangent line to the curve y = 8 / x2 + x + 2 at x = 2.

Q: Figure 14(a) shows a Norman window, which consists

Figure 14(a) shows a Norman window, which consists of a rectangle capped by a semicircular region. Find the value of x such that the perimeter of the window will be 14 feet and the area of the window...

Q: A large soup can is to be designed so that the can

A large soup can is to be designed so that the can will hold 16p cubic inches (about 28 ounces) of soup. [See Fig. 14(b).] Find the values of x and h for which the amount of metal needed is as small a...

Q: In Example 3 we can solve the constraint equation (2)

In Example 3 we can solve the constraint equation (2) for x instead of w to get x = 20 – ½ w. Substituting this for x in (1), we get Sketch the graph of the equation...

Q: A ship uses 5x2 dollars of fuel per hour when traveling at

A ship uses 5x2 dollars of fuel per hour when traveling at a speed of x miles per hour. The other expenses of operating the ship amount to $2000 per hour. What speed minimizes the cost of a 500-mile t...

Q: A cable is to be installed from one corner, C,

A cable is to be installed from one corner, C, of a rectangular factory to a machine, M, on the floor. The cable will run along one edge of the floor from C to a point, P, at a cost of $6 per meter, a...

Q: A rectangular page is to contain 50 square inches of print.

A rectangular page is to contain 50 square inches of print. The page has to have a 1-inch margin on top and at the bottom and a 12-inch margin on each side (see Fig. 16). Find the dimensions of the pa...

Q: Find the point on the graph of y = √x that

Find the point on the graph of y = √x that is closest to the point (2, 0). See Fig. 17. Figure 17: