Question

Find the root of f(x) = exp(x)sin(x) - xcos(x) by the

Newton’s method

starting with an initial value of xo = 1.0.

Solve by using Newton’method until satisfying the tolerance limits of the followings;

i. tolerance = 0.01

ii. tolerance = 0.001

iii. tolerance= 0.0001

Comment on the results!

Answer #2

answered by: anonymous

Let
f(x)=sin(x)+x^3-2. Use the secant method to find a root of f(x)
using initial guesses x0=1 and x1=4. Continue until two consecutive
x values agree in the first 2 decimal places.

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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
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Compute three iterations of Newton Raphson method to find the
root of the following equations
i. f (x) = x3-x-1 with x0 = 2.5
ii. f (x) = sin(2x)-cos(x)-x²-1 with x0 = 2.0
iii. x exp(x) = 2 with x0 = 0.55

17. I am using Newton’s method to ﬁnd the negative root of f(x)
= 3−x2.
(a) What would be a good guess for x1? Draw the line
tangent to f(x) at your x1 and explain why using
Newton’s method would lead to the negative root of the
function.
(b) What would be a bad guess for x1? Draw the line
tangent to f(x) at your x1 and explain why using
Newton’s method would not lead to the negative root of...

Use Newton's method to approximate a root of
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x1 =
x2 =
x3 =
x4 =

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a. Find the root of function ?(?)f(x) starting with
?0=1.0x0=1.0.
b. Compute the ratio |??−?|/|??−1−?|2|xn−r|/|xn−1−r|2, for
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not observe a convergence).

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