Questions:

1. Write the following mathematical expressions in Java.

   
   
   
   

2. Write the following Java expressions in mathematical notation.

   dm = m * ((Math.sqrt(1 + v / c) / Math.sqrt(1 - v / c)) - 1);
   
   volume = Math.PI * r * r * h;
   
   volume = 4 * Math.PI * Math.pow(r, 3) / 3; 

3. What is wrong with this version of the quadratic formula?

   x1 = (-b - Math.sqrt(b * b - 4 * a * c)) / 2 * a; 
   
   x2 = (-b + Math.sqrt(b * b - 4 * a * c)) / 2 * a;

4. Give an example of integer overflow. Would the same example work correctly if you used floating-point? Give an example of a floating-point roundoff error. Would the same example work correctly if you used integers? When using integers, you would of course need to switch to a smaller unit, such as cents instead of dollars or milliliters instead of liters.

5. Let n be an integer and x a floating-point number. Explain the difference between

   n = (int)x;

   and

   n = (int)Math.round(x);

   For what values of x do they give the same result? For what values of x do they give different results? What happens if x is negative?

6. Find at least five syntax errors in the following program.

   public class WarmUpSix { 
     public static void main(String[] args) { 
       System.out.print("This program adds two numbers.),
       x = 5; 
       int y = 3.5;
       System.out.print("The sum of " + x + " and " + y " is: "); 
       System.out.println(x + y)
     }
   }

7. Find at least three logic errors in the following program.

   public class WarmUpSeven { 
     public static void main(String[] args) { 
       ConsoleReader console = new ConsoleReader(System.in);
       int total = 1; 
       System.out.println("Please enter a number:"); 
       int x1 = Integer.parseInt(console.readLine()); 
       total = total + x1; 
       System.out.println("Please enter another number:"); 
       int x2 = Integer.parseInt(console.readLine()); 
       total = total + x1; 
       double average = total / 2;
       System.out.println("The average of two numbers is " 
         + average); 
     }
   }

8. Explain the difference between 2, 2.0, "2", and "2.0".

9. Explain what each of the following two program segments computes:

   x = 2; 
   
   y = x + x;

   and

   s = "2";
   
   t = s + s; 

10. Uninitialized variables can be a serious problem. Should you always initialize every variable with zero? Explain the advantages and disadvantages of such a strategy.

11. True or false? (x is an int and s is a String)
    1. Integer.parseInt("" + x) is the same as x

    2. "" + Integer.parseInt(s) is the same as s

    3. s.substring(0, s.length()) is the same as s

12. Give two ways for converting a number to a string. What is the advantage of each of these ways?

13. How do you get the first character of a string? The last character? How do you remove the first character? The last character?

14. How do you get the last digit of a number? The first digit? That is, if n is 23456, how do you find out 2 and 6? Do not convert the number to a string. Hint: %, Math.log

15. What is a final variable? Can you define a final variable without supplying its value?

16. For the purpose of this exercise, for each of the following cases assume:

    double x = 2.5;
    
    double y = -1.5;
    
    int m = 18;
    
    int n = 4;
    
    String s = "Hello";
    
    String t = "World"; 

    What are the values of the following expressions?
    1. x + n * y - (x + n) * y

    2. m / n + m % n

    3. 5 * x - n / 5

    4. Math.sqrt(Math.sqrt(n))

    5. (int)Math.round(x)

    6. (int)Math.round(x) + (int)Math.round(y)

    7. s + t

    8. s + n

    9. 1 - (1 - (1 - (1 - (1 - n))))

    10. s.substring(1, 3)

    11. s.length() + t.length()