Question

Use Newton's method to derive root of f(x) = sin(x) + 1. What is the order of convergence?

Answer #1

Any doubt in any step then comment below.. i will help you.

Here order of convergence is near 1 ..because roots having multiplicity 2 .. so thts why its order goes to 1...

Use Newton's method to approximate a root of
f(x) = 10x2 + 34x -14 if the initial approximation is
xo = 1
x1 =
x2 =
x3 =
x4 =

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for x > 0 correct to the sixth decimal places. Show all work
below.
(Hint: start with x1 = 2)

Use Newton's method to find the absolute maximum value of the
function f(x) = 8x sin(x), 0 ≤ x ≤ π correct to
SIX decimal places.

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Sketch a picture to illustrate one situation where Newton's
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Solve by using Newton’method until satisfying the tolerance
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i. tolerance = 0.01
ii. tolerance = 0.001
iii. tolerance= 0.0001
Comment on the results!

: Consider f(x) = 3 sin(x2) − x.
1. Use Newton’s Method and initial value x0 = −2 to approximate
a negative root of f(x) up to 4 decimal places.
2. Consider the region bounded by f(x) and the x-axis over the
the interval [r, 0] where r is the answer in the previous part.
Find the volume of the solid obtain by rotating the region about
the y-axis. Round to 4 decimal places.

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