Sessions

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.