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VNIT Maths Numerical Methods Assignment

1. State and prove existence and uniqueness theorem of interpolating polynomials.

2. What is inverse interpolation?

3. Establish Newton's divided difference formula and give an estimate of the remainder term in
terms of the appropriate derivative. Deduce Newton's forward and backward interpolation
formula as particular cases.

4. Obtain error formulas for Lagrange’s interpolation formula.

5. Derive the formula for Hermite interpolation.

6. The function f(x) =