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

    The starting value (x0) is 1 as it lies between x=0 and x=1 when f(x)=0. x0 = 1 x1 = x0 - [(x0 ^4+x0 �-1=0)/( 4x0 �+3x0 �)] = 0.857142857 x2 = x1 - [(x1^4+ x1 �-1=0)/( 4x1 �+3x1 �)] = 0.821252204 x3 = x2 - [(x2^4+x2 �-1=0)/( 4x2 �+3x2

  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)

  1. Mathematics Coursework - OCR A Level

    x-value x-y 0.2509 0.0008579 0.2492 0.001614 0.2523 0.00303 0.2466 0.005714 0.2572 0.01068 0.2369 0.02031 0.2744 0.03749 0.2006 0.07381 0.3322 0.1316 Overflow Overflow - it reached overflow because there are certain x values where there is no point of the graph present.

  2. 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.

  1. GCSE Math Coursework: Triminoes

    +60 +90 +126 +24 +30 +36 +6 +6 Quartic Equation f (n) =an4+bn3+cn2+dn+e n=1 a + b + c + d + e = 6 n=2 16a + 8b + 4c + 2d + e = 30 n=3 81a + 27b + 9c + 3d + e = 90 n=4

  2. Methods of Advanced Mathematics (C3) Coursework.

    If the intervals were smaller then it would have worked. Newton Raphson Method In this method an estimate of the route is taken a line equal to x is taken up until it hits the curve and then a tangent is drawn down to the x-axis.

  1. Change of Sign Method

    x -5 -4 -3 -2 -1 0 1 2 3 4 5 y -155 -79 -31 -5 5 5 1 -1 5 25 65 These show that there are three roots. One between x=-2 and x=-1, one between x=1 and x=2 and another one between x=2 and x=3.

  2. Change of sign method - Finding a root by using change of sign method

    These can be improved the accuracy. Assume X=1.5213 f(x)=(1.5213)^3-1.5213-2=-0.00047 X=1.5214 f(x)=(1.5214)^3-1.5214-2=0.000121 Because the answer is -0.00047<0<0.000121. So the answer must between 1.5213 and 1.5214. However , these are not the exact answer so I have to estimate them. In this case, X=1.5213.5, so the error bound is .

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