Find all the real solutions to cubic equation, Mathematics

Find all the real solutions to cubic equation x^3 + 4x^2 - 10 =0. Use the cubic equation x^3 + 4x^2 - 10 =0 and perform the following call to the bisection method [0, 1, 30]

Use the fixed point iteration to find the fixed point(s) for the function g(x) = 1 + x - x^2/3

Find all the real solutions to cubic equation x^3 +4x^2-10=0. Use the cubic equation x^3 + 4x^2 - 10 =0 and perform the following call to the regulaFalsi [0, 1, 30]

Use newton's method to find the three roots of a cubic polynomial f(x) = 4x^3 - 15x^2 + 17x-6. Determine the Newton-raphson iteration formula g[x] = x - (f(x)/f'(x)) that is used. Show details of the computation for the starting value p0 = 3.

Use the secant method to find the three roots of cubic polynomial f[x]=4x^3 - 16x^2 + 17x - 4. Determine the secant iterative formula g[x] = x - (f[x]/f'[x]) that is used. Show details of the computation for the starting value p0=3 and p1=2.8

Use appropiate Lagrange interpolating polynomials of degrees one, two, and three to approximate each of the following:

A) f(8.4) if f(8.1)= 16.94410, f(8.3)=17.56492, f(8.6)=18.50515, and f(8.7)=18.82091

B)f(1/3) if f(-0.75)= -0.07181250, f(-0.5) = -0.02475000, f(-0.025) = 0.33493750, and f(0)=18.82091

Use the newton forward divided-difference formula is used to approximate f(0.3) given the following data

X        0.0     0.2     0.4     0.6

F(x)  15.0   21.0   30.0   51.0

Suppose it is discovered that f(0.4) was understand by 10 and f(0.6) was overstated by 5. By what amount should the approximation to f(0.3) be changed?

Using the error formulas

|f(x)-P1(x)| ≤ 1/8 max (f(x))h2, linear interpolation

|f(x)-P2(x)| ≤ 1/9√3 max (f(x))h3, quadratic interpolation

A)  what is an appropriate size for the interpolation table for the function tan x on the interval [0,1] in order that linear interpolation produce an error no larger than 0.5 x 10^6

B)   Answer A)

A) Using taylor series expansions derive the O(h^2) central difference approximation

F'(x)= (f(x+h)-f(x-h))/2h

B)  using richardson extrapolation and taylor series expansions derive the O (h4) derivative approximation

F'(x)= (-f(x+2h)+8f(x+h)-8f(x-h)+f(x-2h))/12h

Consider the richardson table for derivatives in the form step size table

Step size                       table

H                                  D(0,0)

H/2                               D(1,0)        D(1,1)

H/2^2                           D(2,0)        D(2,1)        D(2,2)

H/2^3                           D(3,0)        D(3,1)        D(2,3)        D(3,3)

.

.

Where the central difference formula

(h)   = (f(x+h)-f(x-h)) /2h

Is used to construct the first column using

D(n,0)= (h/2^n)

And the following formula

D(n,m)= (4^mD(n,m-1)-D(n-1,m-1))/4^m-1 (use for hand calculations)

D(n,m-1)+((D(n,m-1)-D(n-1,m-1)/(4^m-1)) (use for programming)

Is used, for n≥m, to obtain entries in other columns in terms of the entry to their left and the entry above this entry. For example, D(2,1) is obtained in terms of D(2,0) and D(1,0) and D(3,2) is obtained in terms of D(3,1) and D(2,1)

A) construct the table for the derivative of tan x at x=0.5. Choose an initial step size of h=1 and calculate 4 rows by hand using a calculator

B) use maple procedure richardson in file richardson.txt to calculate 6 rows of the richardson extrapolation table.

----------------------------------------------------------------------------------------------

# lip.txt:

#Symbolic calculation of LIP

#(Lagrange interpolating polynomial)

#

#Arguments

#

#xp   list [x0,x1,....,xn] of nodes

#yp   list[y0,y1,.....,yn] of function values at nodes

#x     symbolic variable for the polynomial

#

#lists xp amd yp have n+1 elements and begin at subscript 1

#so the interpolating polynomial is of degree n

----------------------------------------------------------------------------------------------

lip := proc(xp,yp,x)

         local n,s,p,k,j;

         N := nops(xp) -1; #nops(xp) gives number of elements in xp

         S := 0;

         For k from 0 to n do

                   P := yp[k+1];

                   For j from 0 to n do

                            If j<>k then

                                     P := p*(x-xp[j+1])/(xp[k+1]-xp[j+1]);

                            Fi;

                   Od;

                   S := s=p;

         Od;

         Return s;

End proc:

Posted Date: 3/1/2013 5:24:15 AM | Location : United States







Related Discussions:- Find all the real solutions to cubic equation, Assignment Help, Ask Question on Find all the real solutions to cubic equation, Get Answer, Expert's Help, Find all the real solutions to cubic equation Discussions

Write discussion on Find all the real solutions to cubic equation
Your posts are moderated
Related Questions
Stuckeyburg is a very small town in rural America. Use the map to approximate the area of the town. a. 40 miles 2 b. 104 miles 2 c. 93.5 miles 2 d. 92 miles 2

Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''s encountered is even or odd.on..

Here we will use the expansion method Firstly lim x-0 log a (1+x)/x firstly using log property we get: lim x-0 log a (1+x)-logx then we change the base of log i.e lim x-0 {l

in a rhomus ABCD the circum radii of triangles ABD and ACD are 12.5 cm and 25cm respetively then find the area of rhombus.

a company''s advertising expenditures average $5,000 per month. Current sales are $29,000 and the saturation sales level is estimated at $42,000. The sales-response constant is $2,

integrate sin(x) dx

I have difficuties in working out those 3D trigomentry problems within teh shortest possible time. Are there any tricks to get through such problems as soon as possible?

Find out the volume of the solid obtained by rotating the region bounded by y = x 2 - 2x and  y = x about the line y = 4 . Solution: Firstly let's get the bounding region & t

I figured out the volume and the width, but I have no idea how to use that information to get the height and the length!

A rectangles lenth is (x+4) and width is (x+3).By adding binomials give its perimiter