Question

: Consider f(x) = 3 sin(x^{2}) − 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.

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.

Consider the region bounded by y = x2, y = 1, and the y-axis,
for x ≥ 0. Find the volume of the solid. The solid obtained by
rotating the region around the y-axis.

Apply Newton's Method to f and initial guess
x0
to calculate
x1, x2, and x3.
(Round your answers to seven decimal places.)
f(x) = 1 − 2x sin(x), x0 = 7

Consider the region bounded by y = sin x and y = − sin x from x
= 0 to x = π.
a) Draw the solid obtained by rotating this region about the
line x = 2π.
b) Which method (washers or shells) is preferable for finding
the volume of this solid? Explain.
c) Determine the volume of the solid

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...

Please answer all question explain. thank you.
(1)Consider the region bounded by y= 5- x^2 and y = 1. (a)
Compute the volume of the solid obtained by rotating this region
about the x-axis.
(b) Set up the integral for the volume of the solid obtained by
rotating this region about the line x = −3. No need to evaluate the
integral, just set it up.
(2) (a) Find the exact (no calculator approximation) average
value of the function f(x)...

Consider the region in the xy-plane bounded by the curves y =
3√x, x = 4 and y = 0.
(a) Draw this region in the plane.
(b) Set up the integral which computes the volume of the solid
obtained by rotating this region about
the x-axis using the cross-section method.
(c) Set up the integral which computes the volume of the solid
obtained by rotating this region about
the y-axis using the shell method.
(d) Set up the integral...

Consider the plane region R bounded by the curve y = x − x 2 and
the x-axis. Set up, but do not evaluate, an integral to find the
volume of the solid generated by rotating R about the line x =
−1

Determining Volumes by the Disk-Washer Method
1. Find the volume of the solid formed by revolving the region
bounded by the graph of f(x) = √sin(x) and the x−axis from 0 ≤ x ≤
π about the x−axis. [f(x)= square root(sin(x))]

Consider the function ?(?) = ?^2 − 3? − 2.
a) Use Newton’s Method to estimate a root for the function given by
the above formula. More precisely: Using the initial value of ?1 =
5, calculate ?3.
b) Solve the quadratic equation ?^2 − 3?− 2 = 0 and compute the
two solutions to 4 decimal places. How do these compare to the
approximate root you computed in part (a) above?
c) Suppose your friend uses Newton’s Method to...

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