• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Maths change of sign coursework

Extracts from this document...

Introduction

                Osaamah Mohammed

Maths A2 Coursework

Change of Sign Method:-

3x3 – 6x + 1 = 0

Sketch: -

image15.pngimage25.pngimage33.pngimage31.pngimage25.pngimage25.pngimage09.pngimage14.pngimage00.pngimage01.png

Looking at the graph we find that the roots lie between these intervals:
[-2,-1]  [0,1]  [1,2]

Finding root interval between [0,1] using a Decimal Search

image03.pngimage32.pngimage04.pngimage02.pngimage34.pngimage06.pngimage05.pngimage06.png

Root [0 , 1]

X1 = 0

...read more.

Middle

image07.png

0.17

-0.005261

Root [0.16 , 0.17]

X

f(X)

0.16

0.052298

0.161

0.046520

0.162

0.040755

0.163

0.034992

0.164

0.029233

0.165

0.023476

0.166

0.017723

0.167

0.011972

0.168

0.0062249

0.169

0.00048043image08.pngimage07.png

0.170

-0.005261

Root [0.169 , 0.170]

X

f(X)

0.1690

0.00048043image07.pngimage08.png

0.1691

-0.0000923852

Root [0.1690 , 0.1691]

X

f(X)

0.1690

0.00048043

0.16901

0.00042299

0.16902

0.00036557

0.16903

0.00030814

0.16904

0.00025071

0.16905

0.00019328

0.16906

0.00013586

0.16907

0.00078427

0.16908

0.00021image08.pngimage07.png

0.16909

-0.000036426

From this method we find that the root lies between[0.16908 , 0.16909]

Root = 0.169085 ± 0.000005

testf (0.16908) = 0.00021

        f (0.16909) = -0.000036426

There is a change

...read more.

Conclusion

Start X1 = 0        Use Xn+1 = 2xn3 + 1
                                      
5

X2 = 2(0)3 + 1 = 0.2      

                  5

X3 = 2(0.2)3 + 1 = 0.216      

                  5

X4 = 2(0.216)3 + 1 = 0.22016      

                  5

X5 = 0.22134

X6= 0.22169

X7 = 0.22179

X8 = 0.22182

X9 = 0.22183                        root to 5 s.f (took 9 iterations)image30.png

X10 = 0.22183

Failure: -

Solve 2x3 – 5x + 1 = 0

Re-arrange this so that “X=….”

  • 2x3 – 5x + 1 = 0

      2x3 +1 = 5x

      2x3 = 5x – 1

      x3 = 5x – 1

                 2

      x = (5x – 1)

                 2

      x = g(x)

Sketch : -

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Core & Pure Mathematics essays

  1. Methods of Advanced Mathematics (C3) Coursework.

    The method was very easy to use due to the power of excel and the ability to copy, paste and fill down within the cells. If it were to be done manually it would be much more difficult due to the equations involved and types of polynomial expressions I was using.

  2. 'Change of Sign Method'

    This can be done with the previously used equation y = x3 - 4x+1 Decimal search First interval x f(x) 0 1 0.1 0.601 0.2 0.208 0.3 -0.173 0.4 -0.536 0.5 -0.875 0.6 -1.184 0.7 -1.457 0.8 -1.688 0.9 -1.871 1 -2 The table shows that the sign changes within the interval 0.2 to 0.3.

  1. Numerical Method (Maths Investigation)

    So, we take the value, 0.61906. Upper Bound = 0.619065 Lower Bound = 0.619055 f(Upper bound) = -4.243 10-6 f(Lower Bound) = 7.185 10-6 Error Bound = 0.619065 - 0.61906 = 0.000005 Hence Approximate Root Value is 0.61906 0.000005

  2. Mathematics Coursework - OCR A Level

    the rearrangement method does not work for this rearrangement of the equation as it cannot calculate the y-value for x=0.332207 and beyond. The above is the graph of y=(3x5-x+0.31)1/2 (blue line) and y=x (red line). The purple line shows the method diverging and then it stops when it cannot work

  1. Arctic Research (Maths Coursework)

    the distance that the plane travels equal to the horizontal distance from base camp to observation site. * It takes no time for the plane to take of or land. * Time is flowing forward at a constant rate. * There is no air resistance or friction except for the wind.

  2. Change of Sign Method

    To find the root I need to work out the iterative formula for the Newton Raphson. This is: Therefore To find the root between x=-1 and x=-2 I will use a =-1 as this is close to the solution and should find the right root.

  1. The method I am going to use to solve x−3x-1=0 is the Change ...

    shown below: The blue line is approaching to the root, and that is the answer of f(x)=0 Rearrangement B: 3x^5+5x�-1=0 x�=(1-3x^5)/5 x=V[(1-3x^5)/5] On Autograph software, I can draw the equation y=g(x)= V[(1-3x^5)/5]and also the line y=x. The graph is shown below: I want to find the intersection of the arrow

  2. Functions Coursework - A2 Maths

    x=1.9 to 1 decimal place This process can be repeated as many times to get the root to a desired number of decimal places. To illustrate the fact that the root lies in the interval [1.8,1.9], part of the graph of y=f(x)

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work