Question

Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomials P1(x), P2(x), Pa(x). b) Evaluate f(2.5) by using Pa(x). c) Obtain a bound for the errors E1(x), E2(x), Es(x) Exercise 7: Consider f(x)- In(x) use the following formula to answer the given questions '(x) +16-30f+16f,- 12h a) Derive the numerical differentiation formula using Taylor Series and find the truncation error b) Approximate f'(1.2) with h-0.05 Exercise 8: Derive the numerical differentiation formula using Taylor Series f(x) (x)-4f(x,-h)+ f(x, - 2h) and define the order of approximation 2h 5000 Exercise 9: Find a curve fit y P)1+Ce for the data and calculate E (P) 3 1 2800 1800 1000 500 y Exercise 10: Find a curve fit y P(x)=Bxe for the data 4 2 1 1800 2800 1000 500 y Exercise 11 Use the following backward formula and the given table )3/(x)-4f(x,-h2)+ f(x, -2H) 2h = to approximate f (1.5) xfx) 3 -4 -2.3 0.5 1 -6.5 1.5 LO Exercise 12: Approximate each integral using the composite trapesoidal rule with M-10 - j a) dx xe d b) -1 Exercise 13: Approximate each integral in Exercise 8 using the composite simpson rule with 9 sample points Exersice 14: Determine the number M and the interval withh h so that the Composite Trapesoidal rule xe dx for M subintervals can be used to compute the given integral with an accuracy of 5x10,

Answer 1

According to rules , wee are allow to do only one question at a time so i do only question 8.. you post others separately.. so that i will able to help you.

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