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using System; class ImplicitlyTypedVar { static void Main() { // These are now implicitly typed variables They // are of type double because their initializing // expressions are of type double var s1 = 40; var s2 = 50; // Now, hypot is implicitly typed Its type is double // because the return type of Sqrt() is double var hypot = MathSqrt( (s1 * s1) + (s2 * s2) ); ConsoleWrite("Hypotenuse of triangle with sides " + s1 + " by " + s2 + " is "); ConsoleWriteLine("{0:####}", hypot); // The following statement will not compile because // s1 is a double and cannot be assigned a decimal value

2x 2 ln2 (|x|) (1 + x 2 )

Part I:

Therefore, the displacement equations of the modi ed sine curve are 1 p q q y = h sin 4p b 4 + p b 4( 4 + p ) 2 p q 9 4p q p + y = h + sin 3 b 3 4 + p 4 + p b 4( 4 + p ) p q 4 1 q y = h 4 + p + 4 + p b - 4( 4 + p ) sin 4p b 0 q

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There is a second use of the fixed keyword that enables you to create fixed-sized, singledimensional arrays In the C# documentation, these are referred to as fixed-size buffers A fixedsize buffer is always a member of a struct The purpose of a fixed-size buffer is to allow the creation of a struct in which the array elements that make up the buffer are contained within the struct Normally, when you include an array member in a struct, only a reference to the array is actually held within the struct By using a fixed-size buffer, you cause the entire array to be contained within the struct This results in a structure that can be used in situations in which the size of a struct is important, such as in mixed-language programming, interfacing to data not created by a C# program, or whenever a nonmanaged struct containing an array is required Fixed-size buffers can be used only within an unsafe context

20:

Evaluating all constants the characteristics equations for the modi ed sine curve are: for 0 q 1 b 8 q q y = h 043990 - 035014 sin 4p b b h q 1 - cos 4p b b h q y = 552796 2 sin 4p b b q h y = 694664 cos 4p b3 b y = 043990

lim ln f (x) = 0

U n s a f e C o d e , P o i n t e r s , N u l l a b l e Ty p e s , a n d M i s c e l l a n e o u s To p i c s

To create a fixed-size buffer, use this form of fixed: xed type buf-name[size];

1 q 7 8 b 8 q 4p q p - y = h 028005 + 043990 - 0351506 cos 3 b 3 b h 4p q p + y = 043990 + 131970 sin 3 b 3 b y = 552796 y = 231555 7 q 1 8 b q q y = h 056010 + 043990 - 003515006 sin 4p b b h q y = 043989 1 - cos 4p b b q h sin 4p b2 b q h y = 694664 3 cos 4p b b y = 552796 h 4p q p + sin 3 b 3 b2 h 4p q p + cos 3 b 4 b3

Here, type is the data type of the array; buf-name is the name of the fixed-size buffer; and size is the number of elements in the buffer Fixed-size buffers can be specified only within a struct To understand why a fixed-size buffer might be useful, consider a situation in which you want to pass bank account information to an account management program that is written in C++ Furthermore, assume that each account record uses the following organization:

Name Balance ID An 8-bit, ASCII character string, 80 bytes long A double, 8 bytes long A long, 8 bytes long

You Try It: Evaluate the limit limx 0+ (1/x)x You Try It: Evaluate the limit limx 0+ (1 + x)1/x In fact this limit gives an important way to de ne Euler s constant e (see Sections 19 and 623)

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