MATH 455 Instructions Homework 2 Written assignments are graded based on quality of work and fully worked out solutions Points will be deducted for incomplete reasoning and disorganized work even if your answers are correct a Use Lagrange interpolation to nd a polynomial that passes through the given points 1 Interpolation i 0 1 2 3 3 0 ii 1 0 2 1 3 1 5 2 b Use Newton s divided di erences to nd a polynomial that passes through the given points Do these agree c Find the 2nd degree interpolating polynomial P2 x through the given points and address the questions that with the polynomials found in problem 1 a i 0 1 2 3 3 0 ii 1 0 2 1 3 1 5 2 follow i 0 0 2 1 0 A Calculate P2 4 which should approximate sin 4 B Give an error bound for the approximation provided above C Compare the actual error to your error bound ii 1 0 2 ln 2 4 ln 4 A Use P2 x to approximate ln 3 B Give an error bound for the approximation provided above C Compare the actual error to your error bound d Use Newton s divided di erences to approximate f 0 3 given the following data Suppose it is discovered that f 0 4 was understated by 10 and f 0 6 was overstated by 5 By what amount should the approximation for f 0 3 be changed x 0 0 0 2 0 4 0 6 f x 15 21 30 51 1