Matoshri College of Engineering & Research Centre, Nashik
Matoshri college of Engineering & Research Centre, Nashik
Interpolation
1. The process of finding the values inside the interval(X0, Xn) is called.
A. Interpolation
B. Extrapolation
C. Iterative
D. Polynomial equation
Difference operators
1. The forward difference operator is denoted by the symbol ______.
A. ∆ B. Ω
C. ∂ D. ∞
2. The Delta of power two is called the ____order difference operator.
A. First B. second
C. Third D. Fourth
Newton’s forward interpolation formula
1. To get the value y corresponds to x, for the start value (lies between) of the table ______formula is used.
A. Newton Forward Interpolation Formula
B. Newton Backward Interpolation Formula
C. Newton Forward Difference Formula
D. Newton Backward Difference Formula
2. In Newton’s forward interpolation formula the first two terms will give the _____ interpolation.
A. linear B. parabolic
C. hyperbolic D. polynomial equation
3. Newton forward interpolation formula is used for ______intervals.
A. equal B. unequal
C. open D. closed
4. In case of Newton Forward Interpolation Formula which equation is correct to find u.
A. x – x0 = uh B. x + x0 = uh
C. x – x0 = u D. (x – x0 )h = u
5. For the given distributed data find the value of Δ3y0 is?
x / 3.60 / 3.65 / 3.70 / 3.75y / 36.598 / 38.475 / 40.447 / 42.521
A. 0.095 B. 0.007
C. 1.872 D. 0.123
Newton’s backward interpolation formula
1. To get the value y corresponds to x, for the end value (lies between) of the table _____ formula is used.
A. Newton Forward Interpolation Formula
B. Newton Backward Interpolation Formula
C. Newton Forward Difference Formula
D. Newton Backward Difference Formula
2. Which methods are best suited for finding a set of interpolation polynomials for increasing values of r?
A. Newton forward and backward interpolation formula
B. Newton Backward difference formula
C. Lagrange's interpolation formula
D. Newton divided difference formula
3. By using Newton’s backward difference table form the following data:
f(30) = 0.5000, f(35) = 0.5736, f(40) = 0.6428, f(45) = 0.7071. What is the value of ∇3yn .
A. - 0.0049 B. - 0.0005
C. -1.872 D. -0.0469
4. In case of Newton Backward Interpolation Formula which equation is correct to find u.
A. x – xn = uh B. x + xn = uh
C. x – xn = u D. (x – xn )h = u
Stirling’s and Bessel’s central difference formula
1. To get the value y corresponds to x, for the middle value (lies between) of the table ___ formula is used.
A. Newton Forward Interpolation Formula
B. Newton Backward Interpolation Formula
C. Central Difference Formula
D. Newton Backward Difference Formula
Newton’s divided difference formula
1. By using Newton’s divided difference table form the following data, what is the value of ▲2y0 .
X / 1 / 2 / 4 / 7 / 12Y / 22 / 30 / 82 / 106 / 216
A. 16 B. 6
C. 1.6 D. 0.194
2. For unequal intervals, to get the value y corresponds to x, we can use....
A. Newton Forward Interpolation Formula
B. Newton Backward Interpolation Formula
C. Lagrange's Interpolation Formula
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
2. Given that ƒ(1) = 2, ƒ(3) = 4, ƒ(5) = 8, ƒ(9) = 16. Find the value of ƒ(6) with the help of Lagrange’s interpolation formula
A. 16 B. 6
C. 1.6 D. 0.194
Numerical Differentiation
Using Newton’s forward formula.
Backward Interpolation formula.
Numerical differentiation can be used only when the difference of some order are ______.
A. equally spaced B. unequally spaced
C. constant D. independent
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 scheme is
A. 0 B. 1.5
C. 2.0 D. 3.0
20. The second order of numerical differentiaon in the Newton’s forward formula for with a step size h is
A. h B. h2
C. h3 D. h4
Numerical Methods & C Programming Unit - 4 Page 2