**Unformatted text preview: **f ( x ) = e x in the interval [0 , 1]. What is the error in your approximation? How could one get a more accurate formula? Additional problem 2: Some of you might be familiar with the formula: n X i =1 i := 1 + 2 + ··· + n = n ( n + 1) 2 . We want to generalize this formula to the sum of squares. Assume that there exists a polynomial, p ( x ), such that n X i =1 i 2 := 1 + 2 2 + ··· + n 2 = p ( n ) . Use Newton’s interpolation to ﬁnd this polynomial. Check your answer by computing the sum of the ﬁrst 100 squares. 1...

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- Fall '08
- Staff
- Numerical Analysis, Addition, additional problem, Newton interpolation polynomial