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calls to start unraveling As they do, the first character of str in each call is displayed This results in the string being displayed in reverse order Recursive versions of many routines may execute a bit more slowly than the iterative equivalent because of the added overhead of the additional method calls Too many recursive calls to a method could cause a stack overrun Because storage for parameters and local variables is on the stack, and each new call creates a new copy of these variables, it is possible that the stack could be exhausted If this occurs, the CLR will throw an exception However, you probably will not have to worry about this unless a recursive routine runs wild The main advantage to recursion is that some types of algorithms can be more clearly and simply implemented recursively than iteratively For example, the quicksort sorting algorithm is quite difficult to implement in an iterative way Also, some problems, especially AI-related ones, seem to lend themselves to recursive solutions When writing recursive methods, you must have a conditional statement, such as an if, somewhere to force the method to return without the recursive call being executed If you don t do this, once you call the method, it will never return This type of error is very common when developing recursive methods Use WriteLine( ) statements liberally so that you can watch what is going on and abort execution if you see that you have made a mistake

the non-trivial fact, explored in 5, that limx 0 x x = 1] t 2 5t + 6 = lim(t 3) = 1 (e) lim t 2 t 2 t 2 (f) lim s 2 2s 3 = lim(s + 1) = 4 s 3 s 3 s 3

There will be times when you will want to define a class member that will be used independently of any object of that class Normally, a class member must be accessed through an object of its class, but it is possible to create a member that can be used by itself, without reference to a specific instance To create such a member, precede its declaration with the keyword static When a member is declared static, it can be accessed before any objects of its class are created and without reference to any object You can declare both methods and variables to be static The most common example of a static member is Main( ), which is declared static because it must be called by the operating system when your program begins Outside the class, to use a static member, you must specify the name of its class followed by the dot operator No object needs to be created In fact, a static member cannot be accessed through an object reference It must be accessed through its class name For example, if you want to assign the value 10 to a static variable called count that is part of a class called Timer, use this line:

Timercount = 10;

This format is similar to that used to access normal instance variables through an object, except that the class name is used A static method can be called in the same way by use of the dot operator on the name of the class Variables declared as static are, essentially, global variables When objects of its class are declared, no copy of a static variable is made Instead, all instances of the class share the same static variable A static variable is initialized before its class is used If no explicit initializer is specified, it is initialized to zero for numeric types, null in the case of reference types, or false for variables of type bool Thus, a static variable always has a value The difference between a static method and a normal method is that the static method can be called through its class name, without any instance of that class being created You have seen an example of this already: the Sqrt( ) method, which is a static method within C# s SystemMath class

delivering good news My arguments are compelling I ranked that question a 5 Tally them up and my score totals 115, quite informal It was good for me to know that an informal approach was appropriate

Part I:

ln(x/2) = lim ln[(x/2)1/(x 2) ] = lim ln(1 + h/2)1/ h = x 2 x 2 x 2 h 0 lim ln[(1 + h/2)2/ h ]1/2 ln e 1/2 = 1/2 [Here we use the non-trivial

Here is an example that declares a static variable and a static method: