Let f(x) = x − 1 + 1/4 cosx = 0 a. Show that f(x) admits only one root ? ∈ [0,1]. b. In order, to approximate r, make 1 iteration using Newton’s method choosing x0 = 0. c. Consider the following method of fixed point xn+1 = g(xn) with g(xn) = 1 −1/4 cos(xn) i. Show that this method converges to r. ii. Determine an approximated value of r such that the error is less than 10^−1 .(choose x0 = 0.2) Newton Raphson formula: xn+1 = xn - f(x)/f'(x)
Let f(x) = x − 1 + 1/4 cosx = 0 a. Show that f(x) admits only one root ? ∈ [0,1]. b. In order, to approximate r, make 1 iteration using Newton’s method choosing x0 = 0. c. Consider the following method of fixed point xn+1 = g(xn) with g(xn) = 1 −1/4 cos(xn) i. Show that this method converges to r. ii. Determine an approximated value of r such that the error is less than 10^−1 .(choose x0 = 0.2) Newton Raphson formula: xn+1 = xn - f(x)/f'(x)
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Let f(x) = x − 1 + 1/4 cosx = 0
a. Show that f(x) admits only one root ? ∈ [0,1].
b. In order, to approximate r, make 1 iteration using Newton’s method choosing x0 = 0.
c. Consider the following method of fixed point xn+1 = g(xn) with g(xn) = 1 −1/4 cos(xn)
i. Show that this method converges to r.
ii. Determine an approximated value of r such that the error is less than 10^−1 .(choose x0 = 0.2)
Newton Raphson formula: xn+1 = xn - f(x)/f'(x)
![Let
f(x) = x - 1+²=cosx = 0
a. Show that f(x) admits only one root r € [0,1].
b. In order, to approximate r, make 1 iteration using Newton's method choosing xo = 0.
c. Consider the following method of fixed point xn+1 = g(xn) with
g(xn) = 1- cos(x₂)
i.
ii.
Show that this method converges to r.
Determine an approximated value ofr such that the error is less than
10-1. (choose xo = 0.2)
Newton Raphson formula: Xn+1 = Xn-
f(x)
fi(x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadae0aba-5d6a-460e-9444-9b07a6803c05%2F387e7e74-7b1a-4eb2-a949-7f5a297a4b6b%2Fvrob8zl_processed.png&w=3840&q=75)
Transcribed Image Text:Let
f(x) = x - 1+²=cosx = 0
a. Show that f(x) admits only one root r € [0,1].
b. In order, to approximate r, make 1 iteration using Newton's method choosing xo = 0.
c. Consider the following method of fixed point xn+1 = g(xn) with
g(xn) = 1- cos(x₂)
i.
ii.
Show that this method converges to r.
Determine an approximated value ofr such that the error is less than
10-1. (choose xo = 0.2)
Newton Raphson formula: Xn+1 = Xn-
f(x)
fi(x)
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