Exercise 1

Write a while loop which print numbers from 0 to 20 in increasing order without using the instruction if:

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Same question but in decreasing order:

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Exercise 2

What is the below program doing?:

a, b, c = 1, 1, 1
while c < 11 :
    print(c, ": ", b)
    a, b, c = b, a+b, c+1

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Exercise 3

Using a while loop, write a function orbit_product_of_digits(n) which returns the list of successive iterations of the function which returns the product of digits, that is, [n, product_of_digits(n), product_of_digits(product_of_digits(n)), ..., z] until a computed number z<10 is reached that can be written with only one digit:

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Can you find a number n such that the length of the orbit is larger than 5?:

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... larger than 10?:

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Exercise 4

The Taylor series of sin(x) is

Write a function taylor_sin(x) which evaluates the Taylor series neglecting the terms of the sums that are less than 10^− 5 in absolute value:

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