Jump to level 1 Fill in the missing numbers of the sequence generated by Euclid's algorithm on inputs 77 and 42. gcd(77, 42) yields sequence: 77 42 Ex: 5 Ex: 5 0

Q10A. Consider the following algorithm: 81 = 3 82 = 8 for k > 2: gk = (k-1)·gk-1 - 8k-2 What is term g6 of the recursive sequence generated as a result of executing this algorithm?

For each whole number n, explain why there exists x with (2n − 1)π/2 < x < (2n + 1)π/2 such that tan(x) = x. Problem 2. For all x ∈ (0, ∞), define f(x) = (1 + x)1/x. Write a table of values of f (x) for x = 1, 10, 100, 1000, and guess limx→∞ f (x). If the limit exists, explain why it must be ≥ 1

Jump to level 1 Fill in the missing numbers of the sequence generated by Euclid's algorithm on inputs 58 and 10. gcd(58, 10) yields sequence: 58 10 Ex: 5 Ex: 5