Question

using newtons method to find the second and third root
approximations of

2x^7+2x^4+3=0

starting with x1=1 as the initial approximation

Answer #1

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

Using Muller’s method with initial approximations p0 = 0, p1 = 1
and p2 = 2, find the approximation p3 to a root of the equation x^4
− 6 = 0. Write your answer using 4-digit chopping.

Use Newton's method with the specified initial approximation
x1 to find x3, the third
approximation to the root of the given equation.
x3 + 5x − 2 =
0, x1 = 2
Step 1
If
f(x) =
x3 + 5x − 2,
then
f'(x) = _____ x^2 + _____
2- Use Newton's method to find all roots of the
equation correct to six decimal places. (Enter your answers as a
comma-separated list.)
x4 = 5 + x
.

Use Newton’s Method to approximate a critical
number of the function ?(?)=(1/3)?^3−2?+6.
f(x)=1/3x^3−2x+6 near the point ?=1x=1. Find the next two
approximations, ?2 and ?3 using ?1=1. x1=1 as the initial
approximation.

Find the root of the function: f(x)=2x+sin(x)-e^x,
using Newton Method and initial value of 0. Calculate the
approximate error in each step. Use maximum 4 steps (in case you do
not observe a convergence).

Complete four iterations of Newton’s Method for the function
f(x)=x^3+2x+1 using initial guess x1= -.5

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.

Use zero to third order approximations, respectively to
determine f(x) = (4x - 6)3
using base point xi = 2 by Taylor series
expansion. Approximate f(4) and compute true percent
relative error |εt| for each approximation.

Use
the root-solving method to obtain the root of x^4-10x^3-50x+24=0
within the error range of 10^-4. (Put in the initial x^(0)=3.5 /
Please make the significant figure 10^-5.)

Find the derivative of the function G(x)=1/2x^4+5x^3−x^2+6.8x+
square root of 3

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