Answer all questions, working needs to be shown to get full marks.

Let f(x)=2sin?(px)+cos?(px/7)

Compare the results from the four methods listed below, when determining the first positive root, accurate to 3 decimal places, for the f(x):

Fixed point iterative method

ii. Bisection method

iii. Secant method

iv. Newton-Raphson method

[20 marks]

b) Complete the table below of values for f(x) and include in your assignment.

x 0 0.5 1.5 4

f(x)

Determine the polynomial of degree three that interpolates these points.

ii. Use the polynomial to calculate an approximation for f(x)when x=1.

iii. What is the relative error at x=1.

[10 marks]

2. Solve u_(r+2)+?3u?_(r+1)+2u_r=2r-3 given thatu_0=0 and u_1=1 and calculate u_5

[10 marks]

3. Integrate the function

f(x,y)=9x+1y

over the given region R, as shown, where Ris the region bounded by:

y=2x,y=2(7-x), y=(x-7/2)^2+1

[10 marks]

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