Use Theorem 1.6 to determine whether Fixed-Point Iteration of
(a)
(b)
(c)
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- Q9.7 Consider the function f(t) defined as f(t)= 2t^(2) + 8t +9 for the range - < t ≤, and extended periodically. Calculate the following values: X Find f(1.5m) 2(1.5pi)^2 + 8(1.5pi) +9_ Find f(-2π)= 2(-2pi)^2 + 8(-2pi) +9_ Find f(4)= 73 X Find f(10m)=_200pi^(2)+80pi+9_ X Xarrow_forward7) The point p = 3 is a zero of the function f(x) = x³ – 7x? + 15x – 9, using Newton iteration to estimate the zero p = 3, Find the order of convergence R and the asymptotic error constant A .arrow_forwardHere are three different g(x) functions. All are rearrangements of the same f(x). g(x) 4+ 2.x3 - 2x x2 g(x) = /: 4 16 + x³ • g(x) g(x) = 5x2 (a) What is f()? (b) Are there starting values for which one or more of these converge or diverge?arrow_forward
- Find a natural number n such that T * 1(n) = 180.arrow_forwardFind the long run behavior of each of the following functions. If the function goes to ∞ or -∞ enter INFINITY or- INFINITY respectively. (a) As →∞, 10(0.4) (b) Ast-∞, 15(2.8) - (c) As t→∞, 0.2(1-(0.3)¹)→arrow_forwardConsider the function f(x) = Inx+2- whose graph is given below. -1 -2 (a) On the graph, illustrate how Newton-Raphson's method locates x1 start- ing with xo = 4. Compute x1. (b) With xo = 1, will Newton-Raphson's method converge to a root? Illustrate your answer both geometrically-on the graph and algebraicallyarrow_forward
- Derive the 4-point forward formula for f"(x) by using values f(x), f(x+h), f(x+2h), and f(x+3h). Show your work!arrow_forward3. Let f(x) = 8x- 3x*+5 %3! a) Find where f has stationary points. b) Perform a sign analysis on the derivative of f. Find where f is increasing and decreasing. c) Use your results to find where all local maxima and minima of foccur.arrow_forwardlet f(X)=5x +(-3) find the largest & sothat [fx)-F(a]]arrow_forwardFor these questions use the first derivative process to show the second part of the AST condition which shows the function decreasing. Converges or divergesarrow_forwardf(2) = 2x² + x +; 3. a) Show that if you use the newton method on the function f(x) it not converges, instead is being cyclical if you start it with *o = 0 . b) Given function: f(x) = ax? +x+c with a ± 0 and c + 0 Which requirements need the coefficients a and c need to fulfill, in order for the newton method applied to the function f(x) to not converge, but instead being cyclical if you start it with Xo = 0.arrow_forwardA particle is moving along the x-axis such that its velocity, v(t), measured in feet per second, at any given time, t, is graphed in the graph above. Which of the following statements is/are true? The particle is moving to the left on 5arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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