Question

Approximate the fixed point of the function to two decimal
places. [A *fixed point* of a function *f* is a real
number *c* such that

f(c) = c.]

f(x) = 9 cot(x), 0 < x < π

c= ?

Answer #1

please comment if you have any doubts will clarify

Use
Newton's method to approximate the root of the equation to four
decimal places. Start with x 0 =-1 , and show all work
f(x) = x ^ 5 + 10x + 3
Sketch a picture to illustrate one situation where Newton's
method would fail . Assume the function is non-constant
differentiable , and defined for all real numbers

Find n for which the nth iteration by the fixed point method is
guaranteed to approximate the root of f(x) = x − cos x on [0, π/3]
with an accuracy within 10−8 using x0 = π/4
Answer: n = 127 iterations or n = 125 iterations.
Please show work to get to answer

Calculate two iterations of Newton's Method to approximate a
zero of the function using the given initial guess. (Round your
answers to three decimal places.)
45. f(x) = x5 −
5, x1 = 1.4
n
xn
f(xn)
f '(xn)
f(xn)
f '(xn)
xn −
f(xn)
f '(xn)
1
2
40. Find two positive numbers satisfying the given
requirements.
The product is 234 and the sum is a minimum.
smaller value=
larger value=
30.Determine the open intervals on which the graph is...

1. Use a power series to approximate the definite integral, I,
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2. Find a power series representation for the function. (Give
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f(x) = ln(9 − x). Determine the radius of convergence, R. I
already found the first part to be x is 1/n(x/9)^n but can't find
R

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must have a fixed point.[hint: consider the function f(x)-x]
“Recall the intermediate value theorem:suppose that f is
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Use Newton's method to find an approximate answer to the
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Calculate two iterations of Newton's Method to approximate a zero
of the function using the given initial guess. (Round your answers
to four decimal places.)
f(x) = cos x, x1 = 0.8

Calculate two iterations of Newton's Method to approximate a
zero of the function using the given initial guess. (Round your
answers to three decimal places.) f(x) = x3 − 3, x1 = 1.6

Calculate two iterations of Newton's Method to approximate a
zero of the function using the given initial guess. (Round your
answers to four decimal places.)
f(x) = cos x, x1 = 0.8
n
xn
f(xn)
f '(xn)
f(xn)
f '(xn)
xn −
f(xn)
f '(xn)
1
2

i) Approximate the function f(x) = cos x by a Taylor polynomial
of degree 3 at a = π/3
ii) What is the maximum error when π/6 ≤ x ≤ π/2? (this is the
continuation of part i))

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