Activity 1.
Here is how one would use Maple
to verify that
is
unbounded:
>
i:='i': x:='x': y:='y': z:='z':
f := z -> cos(z):
`f(z) ` = f(z);
`f(x + iy) ` = f(x + I*y);
`f(x + iy) ` = evalc(f(x + I*y));
`|f(x + iy)| ` = evalc(abs(f(x + I*y)));
f(0 + i*y) = evalc(f(0 + I*y));
lim := limit(f(0 + I*y), y=infinity):
print(`limit(f(0 + I*y), y=infinity)`,` = `,lim);
Activity
2.
a) Use Liouville’s theorem to prove that
is unbounded. |