Use Theorem 1.6 to determine whether Fixed-Point Iteration of
(a)
(b)
(c)
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Numerical Analysis
- 2. Write the formula for finding a root of f(x) = - x³ –- cos (x), where x is a real positive number, by Newton- Raphson's method. Then, compute the second iteration approximation. Discuss the order of convergence of Newton-Raphson's method.arrow_forwardWe want to find the unique real root of f(x) = x³ + 6x² 40 on the interval [2,3] using the fixed point iteration. Determine whether the fixed point iteration converges for any xo € [2,3], for the given iteration function g(x). (a) g(x) = x³ + 6x² + x − 40 1 2 (b) g(x) = (10—2³) ³ 6 (c) g(x) = x x³+6x²-40 3x²+12xarrow_forwarda) show whether or not fn(x) =sin(x/n) converges poinwise b) show whether or not fn(x) =sin(x/n) converces uniformly . c) show whether or not fn(x) =(1-x)xn converges uniformlyarrow_forward
- The approximation of the root x* of the function f (x) = x* – 5x³ + 9x + 3 in the interval [4,6]accurate to within 10-2 using secant's method starting with xo = 4.5 and x1 = 4.6. Needs 3 iterations Does not converge Needs 2 iterations O Needs 1 iterationarrow_forwardSuppose that a sequence of differentiable functions {fn} converges pointwiseto a function f on an interval [a,b], and the sequence {f′n}converges uniformlyto a function g on [a,b]. Then show that f is differentiable and f′(x) = g(x)on [a,b].arrow_forwardQ9.7 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_forward
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