43) (Trick question) Linear Interpolation gives an answer that a) b) Is not cont

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43) (Trick question) Linear Interpolation gives an answer that a) b) Is not continuous Is continuous but not differentiable c) Has a continuous 1 st derivative but not a 2nd d) All of its derivatives are continuous 44) Spline Interpolation methods use a) Linear approximations b) Low degree ( quadratic/cubic) polynomials c) High order nth degree polynomials d) Intermediate Fibonacci values 45) In order to find the root of a function, through Newton's Method the following must be true of the initial value Xo a) f (Xo)0 b) f' (Xo) 0 c) f (Xo) 0 d) f' (Xo) 0 6) Which method uses a line through two points and finds where it crosses the axis? a) Secant Method b) Gauss Jordan c) Newton's Method d) Taylor's Method 47) Gauss elimination and Cramer's rule can both be used for solving systems of simultaneous equations. Cramer's rule uses a closed form formula for each answer. Gauss elimination isa multistep process. What is the advantage of Gauss? a) It gives more precise answers b) It requires fewer calculations It does not use derivatives but Cramer does c) d) It is easier to program for large systems 48) What does a coefficient of determination (r 2) of 0 mean? The dependent variable CAN NOT be predicted b) a) The dependent variable CAN be predicted with "0 error" c) The independent variable is the true cause of changes in the dependent variable am d) There is collinearity in the data 49) In the Lagrange interpolation method, for a list of n points passing there will be a polynomial of degree at most through the given points a) n b) n-1c) n+l d) 2n 50) What's the best way to determine if a program is giving you the right answers a)) Test the program with several problems for which you b) c) d) already know the answers Rewrite the program in C+ or Java Run hardware diagnostic tests on the computer You never have to worry about this since computers always give the right answer m:

Explanation / Answer

49) optin C is correct

Since Lagrange's interpolation is also an Nth degree polynomial approximation to f(x) and the Nth degree polynomial passing through (N+1) points is unique hence the Lagrange's and Newton's divided difference approximations are one and the same. However, Lagrange's formula is more convinent to use in computer programming and Newton's divided difference formula is more suited for hand calculations.

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