Exercises
- 1.
- Define a = 5. Define b = a2. Evaluate b. Now Define
a =
. Guess the value of b and check
your answer by evaluation.
- 1.
- Define
f (x) = x2 + 3x + 2. Evaluate
and Simplify the result. Do computations in place to show
intermediate steps in the simplification.
- 2.
- Rewrite the function
f (x) = max
x2 -1, 7 - x2
as a
piecewise-defined function.
- 3.
- Experiment with the Euler phi function
(n), which counts
the number of positive integers k≤n such that
gcd(k, n) = 1. Use Define + Define Maple Name to open a dialog box. Type phi(n) as the Maple name,
(n) as the Scientific Notebook
name, and check the Maple Library Numtheory box. Test the statement
``If
gcd(n, m) = 1 then
(nm) =
(n)
(m)'' for several
specific choices of n and m.
- 4.
- Define d (n) by typing divisors(n) as the Maple name, d (n)
as the Scientific Notebook name, and check the Maple
Library Numtheory box. Explain what the function d (n) produces. This is
an example of a set-valued function, since the function values are
sets instead of numbers.