Verify that x = 1/a is a fixed point of the function g(x) x(2 ax). Determine the order of convergence and the asymptotic error constant of the iteration sequence Pn = 9(Pn-1) toward x = 1/a. =
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- Prove that the sequence (xn) = (-1)"+' [3 .does not converge to any real number= (10 points) For the function g(x) = x = (1 + c) x + cx³, show that a 1 is a fixed point and determine for which values of the constant c the iteration sequence for initial conditions sufficiently close to a converge. For what values of c, if any, is the convergence quadratic? Verify your results graphically and numerically.Determine if the sequence bn = (2n2)/ln(n+5) is convergent or divergent. If converges, find the value.
- Suppose a person invested 1 million dollars in a certain project in the beginning of year 2000. The investment is a huge success and is now worth 10 million dollars at the end of year 2020. Assume that the investment has constant growth rate throughout the 20 years. Choose one number k from the set {2,3, •••,9} and find the time interval in which W has leading digit k.When finding the root of equation x²-x²-1=0 near xo=1.5, rewrite it to the following 4 types. Analysis the convergence of them, select the fast convergent one and then calculate the root with error tolerance 10³. (1)x=1+1/2 (3)x= √√√x³-1 (2) x = 3√/1+x² 1 (4)x = -√√x-1Find the limit of the sequence if it converges; otherwise indicate divergence. an = (-1)" Select one: A. 0 B. 1 C. 3 D. Diverges Integrate the function.