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67 Simplify the expressions exp(ln a ln b) and ln(5 exp b) (a) b/a and ln b + 5 (b) a/b and ln 5 + b (c) ab and ln(5b) (d) a/b and b ln 5 (e) b/a and 5 ln b 68 Simplify the expression (a) (b) (c) (d) (e) exp(a b + c) exp(3a 4b + 5c) exp(a + b + c) exp(3a + 2b 5c) exp(2a 3b + 5c) [exp(a)]3 [exp(b)]2 [exp(c)]5

Part I:

Like methods, constructors can also be overloaded Doing so allows you to construct objects in a variety of ways For example, consider the following program:

// Demonstrate an overloaded constructor using System; class MyClass { public int x; public MyClass() { ConsoleWriteLine("Inside MyClass()"); x = 0; } public MyClass(int i) { ConsoleWriteLine("Inside MyClass(int)"); x = i; } public MyClass(double d) { ConsoleWriteLine("Inside MyClass(double)"); x = (int) d; } public MyClass(int i, int j) { ConsoleWriteLine("Inside MyClass(int, int)"); x = i * j; } } class OverloadConsDemo { static void Main() { MyClass t1 = new MyClass(); MyClass t2 = new MyClass(88); MyClass t3 = new MyClass(1723); MyClass t4 = new MyClass(2, 4); ConsoleWriteLine("t1x: ConsoleWriteLine("t2x: ConsoleWriteLine("t3x: ConsoleWriteLine("t4x: } } " " " " + + + + t1x); t2x); t3x); t4x);

69 The derivative of the function f (x) = exp(sin x) is 2 (a) exp(cos x) (2 sin x cos x) (b) exp(sin x) (2 sin x cos x) 2 (c) exp(sin x) (2 sin x) (d) exp(sin x cos x) (2 sin x cos x) 2 (e) exp(sin x) (2 sin x cos x) 70 Calculate the integral (a) exp[tan x] + C (b) exp[cos x] + C (c) exp[sin x] + C exp[sin x] cos x dx

The output from the program is shown here:

Inside Inside Inside Inside MyClass() MyClass(int) MyClass(double) MyClass(int, int)

In the last chapter, we reviewed common grammar, punctuation, word usage, and capitalization errors and discussed strategies to remember the rules In this chapter, you ll put all the tools we ve discussed to work You ll practice writing a report, and you ll compare your approach to another writer s strategy You ll see rsthand how using the three-step process as a framework allows you to work productively

8:

t1x: t2x: t3x: t4x:

(d) exp[sin x] + cos x + C (e) exp[cos x] + sin x + C 71 Calculate [exp(2x)]3 dx (a) [exp(3x)]2 + C (b) [exp(2x)]3 + C (c) [exp(2x)]4 /4 + C (d) [1/6][exp(2x)]3 + C (e) [1/5][exp(2x)]4 + C 72 Simplify ln(e 3 54 ) (a) 3 + 4 ln 5 (b) 3 4 ln 5 ( ) 5 + 3 ln 4 (c) 4 + 5 ln 3 (d) 5 5 ln 5 73 Simplify the expression ln[e 3x 5e ] (a) x + e ln 5 (b) 3x + 3 ln 5 (c) 3x + e ln 5 (d) x e ln 5 (e) 3x + 5 ln e 74 Simplify the expression e 4 ln 7 2 ln 3 (a) 74 /32 (b) 72 /34 (c) 77 /33 (d) 44 /33 (e) 47 /23 75 Calculate log2 8 log3 81 + log5 125 (a) 1 (b) 2 (c) 3 (d) 2 (e) 1 76 Solve the equation 3x 52x = 3/7x for x (a) x = log5 323 (b) x = log3 525

0 88 17 8

MyClass( ) is overloaded four ways, each constructing an object differently The proper constructor is called based upon the arguments specified when new is executed By overloading a class constructor, you give the user of your class flexibility in the way objects are constructed One of the most common reasons that constructors are overloaded is to allow one object to initialize another For example, here is an enhanced version of the Stack class developed earlier that allows one stack to be constructed from another: