5. (10 points) Derive the following formula for f(x) f(4(x+)-3f(x)-f(x+2h)) and show that error is OCh 5. (10 points) Derive the following formula for f(x) f(4(x+)-3f(x)-f(x+2h)) and show th...
Please help me solve this. thanks 5. Using Taylor series, derive the error term for the approximation f' (x) ~ -3 f(x) + 4 f(x + b)-f(x + 2h)]. 2h 5. Using Taylor series, derive the error term for the approximation f' (x) ~ -3 f(x) + 4 f(x + b)-f(x + 2h)]. 2h
Derive the following numerical approximation to the second derivative of f(x) using Taylor's series. Show all of your steps and derive also the order of accuracy of this approximation in terms of h. - f(x + 2h) + 16f(x + h) – 30f(x) + 16 f(x – h) – f(x – 2h) 12h2 1 (C)
2. Show that the approximation 2 1 h) - 5(x- h)- S(x + 2h) - f(x- 2h) (x) can be obtained by a Richardson extrapolation. [Hint: Consider (h) f(z+2h)-f(x-2h) 2h 2. Show that the approximation 2 1 h) - 5(x- h)- S(x + 2h) - f(x- 2h) (x) can be obtained by a Richardson extrapolation. [Hint: Consider (h) f(z+2h)-f(x-2h) 2h
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...
Derive question! Thank you. Derive the E(X) (4 point s)and the var() (5 points each). Show all steps or no credit will be awarded
The variance of f(x) is defined by: varlf]- E[(f(x) E[f(x)])21 Using this formula derive the following:
Find a function f for which 2f(x)-3f-x)= 5-1.
Can't solve the following second order differential equation: f''(x)+3f'(x)+2=4t Show full complementary function and particular integral working out, thanks in advance.
π/2 (6 3 cos x) dx 0 (a) Derive the formula for multi-segment (evenly spaced) left-hand rectangles and then use it to approximate the value of the integral with n=1; n-2; n-4 segments. Calculate the true error and relative true error for each (b) Derive the formula for multi-segment (evenly spaced) right-hand rectangles and then use it to approximate the value of the integral with n=1; n=2; n-4 segments. Calculate the true error and relative true error for each (c)...
5. Find the open Newton-Cotes formula to approximate the integral f(x)dx using two points inside the interval (a,b). Find the absolute error in the ap- proximation 5. Find the open Newton-Cotes formula to approximate the integral f(x)dx using two points inside the interval (a,b). Find the absolute error in the ap- proximation