Question

*Use Newton's method to find an approximate answer to the
question. Round to six decimal places. 2) Where is the first local
maximum of f(x) =3x sin x on the interval (0, Q)
located?*

Answer #1

8. (a) Use Newton's method to find all solutions of the equation
correct to six decimal places. (Enter your answers as a
comma-separated list.) sqrt(x + 4) = x^2 − x 2.
(b) Use Newton's method to find the critical numbers of the
function: f(x) = x^6 − x^4 + 4x^3 − 3x, correct to six decimal
places. (Enter your answers as a comma-separated list.) x =

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

Use Newton's method to find all solutions of the equation
correct to six decimal places. (Enter your answers as a
comma-separated list.)
x + 4
= x2 − x

Use Newton's method to find all the roots of the equation
correct to eight decimal places. Start by drawing a graph to find
initial approximations.
3 sin(x2) = 2x

Use Newton's method to find the
number arcsin(1/3) rounded to 14 digits after the
decimal point by solving numerically the equation sin(x)=1/3 on the
interval [0,pi/6].
1) Determine f(a) and f(b).
2) Find analytically f', f'' and check if f '' is continuous on
the chosen interval [a,b].
3) Determine the sign of f' and f '' on [a,b] using their
plots.
4) Determine using the plot the upper bound C and the lower
bound c for |f'(x)|.
5) Calculate the...

Use Newton's method with the specified initial approximation x1
to find x3, the third approximation to the root of the given
equation. (Round your answer to four decimal places.) 2x^3 − 3x^2 +
2 = 0, x1 = −1

: 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.

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 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

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

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