Ex. 1 → Check whether x = 2.3 is a zero of the function:
Ex. 2 → According to de Moivre's formula, the following holds:
Choose numbers n and x and verify that formula in Python.
Ex. 3 → Complex numbers. Verify Euler's formula in the same way:
Ex. 4 → Suppose we are trying to check the convergence of a diverging sequence (here the sequence is defined by the recursive relation un +1= 2un and u0 = 1.0):
u = 1.0 # you have to use a float here!
uold = 10.
for iteration in range(2000):
if not abs(u-uold) > 1.e-8:
print('Convergence')
break # sequence has converged
uold = u
u = 2*u
else:
print('No convergence')- Since the sequence does not converge, the code should print the
No convergencemessage. Execute it to see what happens. What happens if you replace the line:
if not abs(u-uold) > 1.e-8
with:
if abs(u-uold) < 1.e-8
It should give exactly the same result, shouldn't it? Run the code...
