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To generate a sequence of pseudorandom numbers, you will use the Random class Sequences of random numbers are useful in a variety of situations, including simulations and modeling The starting point of the sequence is determined by a seed value, which can be automatically provided by Random or explicitly specified Random defines these two constructors: public Random( ) public Random(int seed) The first version creates a Random object that uses the system time to compute the seed value The second uses the value of seed as the seed value Random defines the methods shown in Table 21-14 Here is a program that demonstrates Random by creating a pair of computerized dice:

(512)

// An automated pair of dice using System; class RandDice { static void Main() { Random ran = new Random(); ConsoleWrite(ranNext(1, 7) + " "); ConsoleWriteLine(ranNext(1, 7)); } }

21:

j =1

[(ln x)5 ],

Method public virtual int Next( ) public virtual int Next(int upperBound) public virtual int Next(int lowerBound, int upperBound) public virtual void NextBytes(byte[ ] buf)

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Meaning Returns the next random integer, which will be between 0 and Int32MaxValue 1, inclusive Returns the next random integer that is between 0 and upperBound 1, inclusive Returns the next random integer that is between lowerBound and upperBound 1, inclusive Fills buf with a sequence of random integers Each byte in the array will be between 0 and ByteMaxValue 1, inclusive Returns the next random value from the sequence represented as a floating-point number that is greater than or equal to 00 and less than 10 Returns the next random value from the sequence represented as a floating-point number that is greater than or equal to 00 and less than 10 To create a skewed or specialized distribution, override this method in a derived class

The obvious difference between the rational B-spline method and the nonrational B-spline method is the use of rational B-spline basis functions Therefore, the characteristics of rational B-splines and their evaluation must be addressed in detail Evaluation of Rational B-Splines and Their Derivatives A single rational B-spline, Rj,k(x), of order k is de ned as follows (Versprille, 1975; Tiller, 1983):

public virtual double NextDouble( )

protected virtual double Sample( )

[(ln x) (cot x)]

120 4

Here are three sample runs:

5 2 4 4 1 6

2 Velocity (cm/rad) 0

The program works by first creating a Random object Then it requests the two random values, each between 1 and 6, inclusive

SOLUTION For the rst problem, we let u = 4 + x and du/dx = 1 Therefore we have d 1 d 1 ln(4 + x) = (4 + x) = dx 4 + x dx 4+x Similarly, d 3 1 3x 2 1 d (x x) = 3 ln(x 3 x) = 3 dx x x dx x x d 1 d sin x ln(cos x) = (cos x) = dx cos x dx cos x 5(ln x)4 d d 1 [(ln x)5 ] = 5(ln x)4 (ln x) = 5(ln x)4 = dx dx x x d d d [(ln x) (cot x)] = ln x (cot x) + (ln x) cot x dx dx dx 1 = cot x + (ln x) ( csc2 x) x You Try It: What is the derivative of the function ln(x 3 + x 2 ) Now we examine the graph of y = ln x Since d (ln x) = dx d2 (ii) (ln x) = dx (iii) ln(1) = 0, (i) 1 > 0, x d 1 dx x

The GC class encapsulates the garbage-collection facility The methods defined by GC are shown in Table 21-15 It defines the read-only property shown here: public static int MaxGeneration { get; } MaxGeneration contains the maximum generation number available to the system A generation number indicates the age of an allocation Newer allocations have a lower number than older ones Generation numbers help improve the efficiency of the garbage collector For most applications, you will not use any of the capabilities of GC However, in specialized cases, they can be very useful For example, you might want to use Collect( ) to force garbage collection to occur at a time of your choosing Normally, garbage collection occurs at times unspecified by your program Since garbage collection takes time, you might not want it to occur during some time-critical task, or you might want to take advantage of idle time to perform garbage collection and other types of housekeeping chores

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