User-Defined Procedures

1. Write a Scheme procedure (add2 a) that returns the sum a+2.

2. Define a procedure f(x) = x² - 3x + 2 and evaluate it for x = 0, 1, 2, 3, 4 .

3. Write a procedure (quadratic-root a b c) that finds one root of a quadratic equation
   ax² + bx + c = 0 using the quadratic formula. Use it to find a root of the above equation.

   Test your procedure by computing

    
        (quadratic-root 1 -5 6)
        (quadratic-root 2 -10 12)
        (quadratic-root 1 4 4).
   

   In each case, use algebra to check your answers.

   What are (quadratic-root 1 0 1) and (quadratic-root 1 0 2)?
   [Would these two examples work in other programming languages that you know?]

4. Write a procedure swap that interchanges the first two elements on a list, leaving the rest of the list unchanged. Thus, (swap '(a b c d e)) should return (b a c d e). In this problem, assume that the list given to swap has at least two elements; do not worry about the possibility that swap might be applied to numbers, empty lists, or lists with only one element.

5. Textbook Exercises: As you have time, work on exercises 2.1-2.5 from the textbook.

This document is available on the World Wide Web as

http://www.math.grin.edu/~walker/courses/151/lab-procedures.html