Matoshri College of Engineering & Research Centre, Nashik

Matoshri college of Engineering & Research Centre, Nashik

Interpolation 4. In case of Newton Forward Interpolation Formula which equation is correct to find u.

1. The process of finding the values inside the in- A. x – x0 = uh B. x + x0 = uh terval(X0, Xn) is called. C. x – x0 = u D. (x – x0 )h = u

A. Interpolation 5. For the given distributed data find the value 3 B. Extrapolation of Δ y0 is? C. Iterative D. Polynomial equation x 3.60 3.65 3.70 3.75 y 36.598 38.475 40.447 42.521 Difference operators A. 0.095 B. 0.007 1. The forward difference operator is denoted by C. 1.872 D. 0.123 the symbol ______. Newton’s backward interpolation formula A. ∆ B. Ω C. ∂ D. ∞ 1. To get the value y corresponds to x, for the end value (lies between) of the table _____ 2. The Delta of power two is called the ____or- formula is used. der difference operator. A. First B. second A. Newton Forward Interpolation Formula C. Third D. Fourth B. Newton Backward Interpolation Formula C. Newton Forward Difference Formula D. Newton Backward Difference Formula Newton’s forward interpolation formula 2. Which methods are best suited for finding a 1. To get the value y corresponds to x, for the set of interpolation polynomials for increasing start value (lies between) of the table ______values of r? formula is used. A. Newton forward and backward interpolation A. Newton Forward Interpolation Formula formula B. Newton Backward Interpolation Formula B. Newton Backward difference formula C. Newton Forward Difference Formula C. Lagrange's interpolation formula D. Newton Backward Difference Formula D. Newton divided difference formula

2. In Newton’s forward interpolation formula 3. By using Newton’s backward difference table the first two terms will give the _____ form the following data: interpolation. f(30) = 0.5000, f(35) = 0.5736, f(40) = 0.6428,

A. linear B. parabolic 3 C. hyperbolic D. polynomial equation f(45) = 0.7071. What is the value of ∇ yn .

3. Newton forward interpolation formula is used for ______intervals. A. - 0.0049 B. - 0.0005 A. equal B. unequal C. -1.872 D. -0.0469 C. open D. closed 4. In case of Newton Backward Interpolation

Numerical Methods & C Programming Unit - 4 Page 1 Matoshri college of Engineering & Research Centre, Nashik

Formula which equation is correct to find u.

A. x – xn = uh B. x + xn = uh 2. Given that ƒ(1) = 2, ƒ(3) = 4, ƒ(5) = 8, ƒ(9) = 16.

C. x – xn = u D. (x – xn )h = u Find the value of ƒ(6) with the help of Lagrange’s interpolation formula Stirling’s and Bessel’s central difference A. 16 B. 6 formula C. 1.6 D. 0.194 1. To get the value y corresponds to x, for the middle value (lies between) of the table ___ formula is used. Numerical Differentiation

A. Newton Forward Interpolation Formula B. Newton Backward Interpolation Formula Using Newton’s forward formula. C. Central Difference Formula Backward Interpolation formula. D. Newton Backward Difference Formula

Newton’s divided difference formula Numerical differentiation can be used only when the difference of some order are ______. 1. By using Newton’s divided difference table form the following data, what is the value of A. equally spaced B. unequally spaced 2 ▲ y0 . C. constant D. independent X 1 2 4 7 12 Y 22 30 82 106 216 Following are the values of a function y(x) : y(-1) = 5, y(0), y(1) = 8 dy/dx at x = 0 as per Newton's central difference A. 16 B. 6 scheme is C. 1.6 D. 0.194 A. 0 B. 1.5 C. 2.0 D. 3.0 2. For unequal intervals, to get the value y corresponds to x, we can use.... 20. The second order of numerical differentiaon in the Newton’s forward formula for with a step A. Newton Forward Interpolation Formula size h is B. Newton Backward Interpolation Formula A. h B. h2 C. Lagrange's Interpolation Formula C. h3 D. h4 D. Newton Difference Formula

3. Newton’s divided difference formula is used only for ______intervals.

A. equal B. unequal C. open D. closed

Lagrange’s Interpolation

1. Lagrange’s interpolation formula is used to compute the values for ______intervals.

A. equal B. unequal C. open D. closed

Numerical Methods & C Programming Unit - 4 Page 2