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As the preceding example shows, it is not difficult to implement IEnumerator and IEnumerable. However, it can be made even easier through the use of an iterator. An iterator is a method, operator, or accessor that returns the members of a set of objects, one member at a time, from start to finish. For example, assuming some array that has five elements, then an iterator for that array will return those five elements, one at a time. By implementing an iterator, you make it possible for an object of a class to be used in a foreach loop. Let s begin with an example of a simple iterator. The following program is a modified version of the preceding program that uses an iterator rather than explicitly implementing IEnumerator and IEnumerable.

This is a familiar expression (see ( )). As we let h 0, we know that this expression tends to the derivative of at c. On the other hand, it is reasonable to declare this limit to be the instantaneous velocity. We have discovered the following important rule: Let be a differentiable function on an interval (a, b). Suppose that (t) represents the position of a moving body. Let c (a, b). Then (c) = instantaneous velocity of the moving body at c. Now let us consider slope. Look at the graph of the function y = f (x) in Figure 2.6. We wish to determine the slope of the graph at the point x = c. This is the same as determining the slope of the tangent line to the graph of f at x = c, where the tangent line is the line that best approximates the graph at that point. See Figure 2.7. What could this mean After all, it takes two points to determine the slope of a line, yet we are only given the point (c, f (c)) on

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You can determine if an object is of a certain type by using the is operator. Its general form is shown here:

Remember, when an anonymous type is created, the identifiers that you specify become read-only public properties. Thus, they can be used by other parts of your code. Although the term anonymous type is used, it s not quite completely true! The type is anonymous relative to you, the programmer. However, the compiler does give it an internal name. Thus, anonymous types do not violate C# s strong type checking rules. To fully understand the value of anonymous types, consider this rewrite of the previous program that demonstrated join. Recall that in the previous version, a class called Temp was needed to encapsulate the result of the join. Through the use of an anonymous type, this placeholder class is no longer needed and no longer clutters the source code to the program. The output from the program is unchanged from before.

3.2 Maximum/Minimum Problems ......................................................................................................................................

Table 10-1 Commonly Used Exceptions Defined Within the System Namespace One other point: In the fourth Exception constructor shown previously, notice that the types SerializationInfo and StreamingContext are preceded by System.Runtime .Serialization. This specifies the namespace in which they are contained. Namespaces are examined in detail in 14.

Properties have some important restrictions. First, because a property does not define a storage location, it cannot be passed as a ref or out parameter to a method. Second, you cannot overload a property. (You can have two different properties that both access the same variable, but this would be unusual.) Finally, a property should not alter the state of the underlying variable when the get accessor is called. Although this rule is not enforced by the compiler, violating it is semantically wrong. A get operation should be nonintrusive.

Now graph the sin2 curve. Look first at the range from 0 to n. The sin' curve starts at zero when wt = 0 , and goes to 1 when w t = l r / 2 , and then back to zero again when ot = n .

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