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Study Resources (Algebra)

Consider the sequence (y_n)_n greaterthanorequalto 1 defining the Fibonacci numbers. Set y_1 = 1 and y_2 = 1 and the relation y_n+1 = y_n + y_n - 1 for n greaterthanorequalto 2. Compute the first 50 Fibonacci numbers 2/1 up to 2/50 and store the 50 numbers in a column.
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Consider the system X'=AX. Describe the conditions under which the system has a stable manifold and a solution can start in the stable manifold. Prove that the                     solution starting in a stable manifold, stays in this manifold for all times. describe what happens with other solutions as time goes to.
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Consider the limit of the rational function p(x)lq(x). What conclusion can you make if direct substitution produces each expression? Write a short paragraph explaining your results. lim_x rightarrow c p(x)/q(x) = 0/1 lim_x rightarrow c p(x)/q(x) = 1/1 lim_x rightarrow c p(x)/q(x) = 1/0 lim_x rightarrow c p(x)/q(x) = 0/0.
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