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12 A man wants to determine how far below the surface of the earth is the water in a well How can he use the theory of falling bodies to do so 13 A rectangle is to be placed in the first quadrant, with one side on the xaxis and one side on the y-axis, so that the rectangle lies below the line 2x + 3y = 6 What dimensions of the rectangle will give greatest area 14 A rectangular box with square base is to be constructed to hold 120 cubic inches The material for the base and the top costs 8 cents per square inch and the material for the sides costs 16 cents per square inch What dimensions will give the most economical box 15 Sketch the graph of the function f (x) = [x 2 4]/[x 2 + 4] Exhibit maxima, minima, and concavity 16 On the planet Glug, the acceleration due to gravity of a falling body near the surface of the planet is 12 ft/sec A body is dropped from height 50 feet How long will it take that body to hit the surface of Glug

public int Length { get; private set; }

Because set is private, Length can be set only by code within its class Outside its class, an attempt to change Length is illegal Thus, outside its class, Length is effectively read-only The same technique can also be applied to the Error property, like this:

public bool Error { get; private set; }

Besides the derivative, the other big idea in calculus is the integral A way of adding or amalgamating infinite quantities, integration is a powerful tool in mathematical physics, engineering, and many other disciplines Central to the importance of the integral is the Fundamental Theorem of Calculus---which links differentiation and integration The fact that we can use the derivative to compute the integral changes the face of the subject

This allows Error to be read, but not set, by code outside FailSoftArray To try the auto-implemented version of Length and Error with FailSoftArray, first remove the len and ErrFlag variables They are no longer needed Then, replace each use of len inside FailSoftArray with Length and each use of ErrFlag with Error Here is the updated version of FailSoftArray along with a Main( ) method to demonstrate it: