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[D] (8pts) Consider the recursively defined function below. F(1)=2, F(2) = 1, and F(n) = F(n-1)...
1. The following function t(n) is defined recursively as: 1, n=1 t(n) = 43, n=2 -2t(n-1) + 15t(n-2), n> 3 1. Compute t(3) and t(4). [2 marks] 2. Find a general non-recursive formula for the recurrence. [5 marks] 3. Find the particular solution which satisfies the initial conditions t(1) = 1 and t(2) = 43. [5 marks] 2. Consider the following Venn diagram, illustrating the Universal Set &, and the sets A, and C. А B cat,pig mouse, horse camel...
Find f(1), f(2), f(3), f(4) and f(5) if f(n) is defined recursively by f(0)=3 and for n=0, 1, 2, ... f(n + 1) = 3f(n) + 7 f(n + 1) = f(n)^2 - 2f(n) - 2
PROVE BY INDUCTION Prove the following statements: (a) If bn is recursively defined by bn = bn-1 + 3 for all integers n > 1 and bo = 2, then bn = 3n + 2 for all n > 0. (b) If an is recursively defined by cn = 3Cn-1 + 1 for all integers n > 1 and Co = 0, then cn = (3” – 1)/2 for all n > 0. (c) If dn is recursively defined by...
(1 point) Find the first six terms of the recursively defined sequence 251/2 n-1 Sn = for n > 1, and s1 = 1. 4. first six terms = (Enter your answer as a comma-separated list.)
1. Consider the sequence defined recursively by ao = ], Ant1 = V4 an – An, n > 1. (a) Compute ai, a2, and a3. (b) For f(x) = V 4x – x, find all solutions of f(x) = x and list all intervals where: i. f(x) > x ii. f(x) < x iii. f(x) is increasing iv. f(x) is deceasing (c) Using induction, show that an € [0, 1] for all n. (d) Show that an is an increasing...
Evaluate the piecewise defined function at the indicated values (x2 f(x) if x -1 6x if 1 < x s 1 = -1 if x > 1 f(-3) (- 3 2 f(-1) f(0) = f(30) =
5. Let be the function defined by f(x) = -1 3 1.5 if r <0 if 0<x<2 if 3 < r <5 Find the Lebesgue integral of f over (-10,10).
Find f(1), f(2), and f(3) if f(n) is defined recursively by f(0) = 1 and for n = 0, 1, 2, . . .• f(n+1) = f(n) + 2So, would it be f(n) = f(n+1) + 2? Or would I just keep it like the original and plug in 1, 2, 3. Thanks for any helpful replies.
Problem 5.1.3. Prove by induction on n that (1+ n < n for every integer n > 3.
Assume that the sequence defined by a1 = 3 an+1 = 15-2·an is decreasing and an > O for all n. Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)