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Since its original 10 release, C# has been evolving at a rapid pace Not long after C# 10, Microsoft released version 11 It contained many minor tweaks but added no major features However, the situation was much different with the release of C# 20 C# 20 was a watershed event in the lifecycle of C# because it added many new features, such as generics, partial types, and anonymous methods, that fundamentally expanded the scope, power, and range of the language Version 20 firmly put C# at the forefront of computer language development It also demonstrated Microsoft s long-term commitment to the language The next major release of C# was 30, and this is the version of C# described by this book Because of the many new features added by C# 20, one might have expected the development of C# to slow a bit, just to let programmers catch up, but this was not the case With the release of C# 30, Microsoft once again put C# on the cutting edge of language design, this time adding a set of innovative features that redefined the programming landscape Here is a list of what 30 has added to the language: Anonymous types Auto-implemented properties Extension methods Implicitly typed variables Lambda expressions Language-integrated query (LINQ) Object and collection initializers Partial methods Although all of these features are important and have significant impact on the language, the two that are the most exciting are language-integrated query (LINQ) and lambda expressions LINQ enables you to write database-style queries using C# programming elements However, the LINQ syntax is not limited to only databases It can also be used with arrays and collections Thus, LINQ offers a new way to approach several common programming tasks Lambda expressions are often used in LINQ expressions, but can also be used elsewhere They implement a functional-style syntax that uses the lambda operator => Together, LINQ and lambda expressions add an entirely new dimension to C# programming Throughout the course of this book, you will see how these features are revolutionizing the way that C# code is written.

Let point p and q be the intersection of N1 and N2 on the line of follower motion From statics the sum of the moments is

C# defines the following arithmetic operators:

Operator + * / % ++ Meaning Addition Subtraction (also unary minus) Multiplication Division Modulus Increment Decrement

2 2

(62) (63)

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The operators +, , *, and / all work in the expected way These can be applied to any builtin numeric data type Although the actions of arithmetic operators are well known to all readers, a few special situations warrant some explanation First, remember that when / is applied to an integer, any remainder will be truncated; for example, 10/3 will equal 3 in integer division You can obtain the remainder of this division by using the modulus operator, % The % is also referred to as the remainder operator It yields the remainder of an integer division For example, 10 % 3 is 1 In C#, the % can be applied to both integer and floating-point types

Part I:

Simplifying Eq (62) and Eq (63) and assuming mN1W and mN2W equal zero since they are negligible yields N1 = N1 = A F sina B (64) (65)

Thus, 100 % 30 is also 1 (This differs from C/C++, which allow modulus operations only on integer types) The following program demonstrates the modulus operator:

Notice that even though the sine function takes the value 3/2 at many different values of the variable x, the function Sine takes this value only at x = /3 Similar comments apply to the other two examples We also have 5 3 1 Cos = , 2 6 Cos 1 0 = , 2 2 Cos 1 = 2 4 We calculate the derivative of f (t) = Sin 1 t by using the usual trick for inverse functions The result is d 1 1 (Sin 1 (x)) = = dx 1 x2 1 sin2 (Sin 1 x) The derivative of the function Cos 1 t is calculated much like that of Sin 1 t We nd that d 1 (Cos 1 (x)) = dx 1 x2 EXAMPLE 636

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