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Question: there is no more info needed if thats the conclusion...

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2. (5 pts.) Show that Simpsons Rule is exact for any polynomial of degree n < 3. Use N 3 and integrate from 0 to 1 for convenience 3. (5 pts.) Compare the exact value of the integral f x*dx with the Trapezoid approximation using N-3 and also N-5, and with Simpsons approximation using N-3 points. Use a calculator. 4. (5 pts.) Use Taylor expansions for f(r+h) and f(x+2h) to derive a one-sided expression for the derivative f(x) in terms of f(x), f(x+h) and f(x+2h), where the neglected terms are O(h2) 5. (5 pts.) Derive the Three-Point formula given in class for the derivative of a function with non-uniform grid spacing where h+1-,. Start by writing Taylor expansions for f+i and fi-1 (see Class Notes) 6. (10 pts.) Derive Simpsons Rule for integration using the method of undetermined coef- ficients. 7. (10 pts.) Verify the Richardson Extrapolation Scheme for f() to order O(h6) Recall that Ді (h)-[f(x + h) _ f(x-A)1/2ћ. You may either use Taylor series directly or apply the recursion formula shown in class

There is no more INFO needed, if that's the conclusion you arrive to, you are as lost as I am in this topic.

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