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As the output shows, the cast of MathSqrt( ) to int results in the whole number component of the value In this expression

MathSqrt(n) - (int) MathSqrt(n)

the cast to int obtains the whole number component, which is then subtracted from the complete value, yielding the fractional component Thus, the outcome of the expression is double Only the value of the second call to MathSqrt( ) is cast to int

Ben Franklin once wrote, Never use a longer word when a shorter word will do Brevity is a virtue in business writing Impatient executives, time-strapped managers, and overloaded workers want you to get to

# provides an extensive set of operators that give the programmer detailed control over the construction and evaluation of expressions Most of C# s operators fall into the following categories: arithmetic, bitwise, relational, and logical These operators are examined in this chapter Also discussed are the assignment operator and the operator C# also defines several other operators that handle specialized situations, such as array indexing, member access, and the lambda operator These special operators are examined later in this book, when the features to which they apply are described

1 If possible, use l H opital s Rule to evaluate each of the following limits In each case, check carefully that the hypotheses of l H opital s Rule apply a lim b lim c lim d lim e lim cos x 1 4 2 x 0 x + x e 2x 1 2x x2 + x6 x 0 cos x 3 x 0 x [ln x]2 2 x 1 (x 1) (x 2)4 x 2 sin(x 2) (x 2) ex 1 x2 1

// Demonstrate ICloneable using System; class X { public int a; public X(int x) { a = x; } } class Test : ICloneable { public X o; public int b; public Test(int x, int y) { o = new X(x); b = y; } public void Show(string name) { ConsoleWrite(name + " values are "); ConsoleWriteLine("oa: {0}, b: {1}", oa, b); } // Make a deep copy of the invoking object public object Clone() { Test temp = new Test(oa, b); return temp; } } class CloneDemo { static void Main() { Test ob1 = new Test(10, 20); ob1Show("ob1"); ConsoleWriteLine("Make ob2 a clone of ob1"); Test ob2 = (Test) ob1Clone(); ob2Show("ob2"); ConsoleWriteLine("Changing ob1oa to 99 and ob1b to 88"); ob1oa = 99; ob1b = 88; ob1Show("ob1"); ob2Show("ob2"); } }

The output is shown here:

Part II:

2 If possible, use l H opital s Rule to evaluate each of the following limits In each case, check carefully that the hypotheses of l H opital s Rule apply x3 x 2 x + e 1 x x /2 ln x 2 x + x e 2x x + ln[x/(x + 1)] sin x 2x x + e ex 2 x 1/x ln |x| 2x x e

ob2 values are oa: Changing ob1oa to ob1 values are oa: ob2 values are oa:

10, b: 99 and 99, b: 10, b:

As the output shows, ob2 is a clone of ob1, but ob1 and ob2 are completely separate objects Changing one does not affect the other This is accomplished by constructing a new Test object, which allocates a new X object for the copy The new X instance is given the same value as the X object in the original To implement a shallow copy, simply have Clone( ) call MemberwiseClone( ) defined by Object For example, try changing Clone( ) in the preceding program as shown here:

// Make a shallow copy of the invoking object public object Clone() { Test temp = (Test) MemberwiseClone(); return temp; }