In the process of Numerical Differentiation, we differentiate an interpolating polynomial in place of ------------.

• A) actual function
• B) Lagrange’s polynomial
• C) Newton’s Divided Difference Interpolating polynomial
• D) extrapolating polynomial

Let $$f(x,y) = 2{x^3} + 6{y^3} + 9xy$$ For x=0, 1,2,3,4, and y=0, 1,2,3,4 Then computing the value of f(2.5,3.5) is an example of .......

• A) Interpolation in one dimension
• B) Interpolation in four dimensions
• C) Interpolation in two dimensions
• D) Interpolation in three dimensions

In Simpson’s rule, we assume that f(x) is continuous on [a, b] and we divide [a, b] into an ………… number n of subintervals of equal length.

• A) None of the given choices
• B) Prime
• C) Odd
• D) Even

In Simpson’s 3/8 rule, the global error is of ………………

• A) O(h4)
• B) None of the given choices
• C) O(h3)
• D) O(h2)

Simpson’s 1/3 rule is based on fitting three points with a ………………

• A) Quadratic
• B) Cubic
• C)
• D)

Which of the following is the Cote’s number (weighting coefficient) for the function:
f(x) = x+1 in the interval [0,1]?

• A) -1/2
• B) -3/2
• C) 3/2
• D) 1/2

In Simpson’s rule, we can estimate the integral by …………the areas under the parabolic arcs through three successive points.

• A) Subtracting
• B) None of the given choices
• C) Adding
• D) Multiplying

Which of the following is the Global Error for Trapezoidal’s Rule while integrating
f(x) = x^2 in the interval of [0,2] of equally spaced subinterval of width h =1 and intermediate point x=1?

• A) -1/2
• B) 1/3
• C) 1/2
• D) -1/3

If f(x) = 2x, then which of the following is will be derivative of f(x) at x = 0.2?

• A) 2
• B) 0.4
• C) 0.2
• D) -2

If y(x) is approximated by a polynomial ${P_n}(x)$ of degree n then the error is given by

• A) $$\varepsilon (x) = y(x) - {P_n}(x)$$
• B) $$\varepsilon (x) = y(x)\,\, \times \,\,{P_n}(x)$$
• C) $$\varepsilon (x) = y(x)\,\, \div \,\,\,{P_n}(x)$$
• D) $$\varepsilon (x) = y(x) + {P_n}(x)$$

At which of the following points the Minimum value of 2nd derivative of function
f(x) = -(2/x) in the interval:[1,4] exits?

• A) At x=2
• B) At x=3
• C) At x=4
• D) At x=1

Simpson’s rule is a numerical method that approximates the value of a definite integral by using …………polynomials.

• A) Quadratic
• B) None of the given choices
• C) Linear
• D) Cubic

If [Math Processing Error]$f(x) = 2{x^3} - 5{x^2} + 9x - 6$ , then its------derivative is zero for all x.

• A) 2nd
• B) 5th
• C) 4th
• D) 3rd

\begin{gathered} What\,will\,be\,the\,value\,of\,'a'\,in\,the\,given\,divide\,difference\,table? \hfill \\\ \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D}&{3rdD.D} \\\\ 2&{0.5}&{0.3}&a&{} \\\\ 4&{1.1}&{0.3}&{ - 0.0125}&{ - 0.0021} \\\\ 6&{1.7}&{0.25}&{}&{} \\\\ 8&{2..2}&{}&{}&{} \end{array} \hfill \\\\ \end{gathered}

• A) 0.0612
• B) 0
• C) 0.0115
• D) 0.0893

To evaluate a definite integral of tabular function f(x), piecewise linear approximation led to ---------.

• A) Simpson’s 3/8 Rule
• B) Trapezoidal Method
• C) Romberg’s Method
• D) Simpson’s 1/3 Rule

\begin{gathered} For\,the\,given\,divide\,difference\,table \hfill \\ \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 2&{2.2}&{0.325}&{} \\\ 6&{3.5}&{0.15}&{ - 0.0219} \\\ {10}&{4.1}&{}&{} \end{array} \hfill \\ the\,Newton's\,divide\,difference\,\,{\text{interpolation}}\,formula\,will\,be \hfill \\\ \end{gathered}

• A) y = f(x) = 2.2 + (x - 2)(0.325) + (x - 2)((x - 6)( - 0.0219)
• B) y = f(x) = 2.2 + (x - 6)(0.325) + (x - 12)((x - 6)( - 0.0219)
• C) y = f(x) = 2.2 + (x - 12)(0.325) + (x - 6)((x - 2)( - 0.0219)
• D) y = f(x) = 2.2 + (x - 2)((x - 6)(0.325) + (x - 2)( - 0.0219)

While employing Trapezoidal and Simpson Rules to evaluate the double integral numerically, by using Trapezoidal and Simpson rule with respect to -------- variable/variables at time

• A) both
• B) single
• C)
• D)

For\,the\,given\,data\,{\text{points}}\,(2,5),\,(4,7),\,and\,(6,9),\,the\,{\text{first}} - order\,divide\,difference\,will\,be\,

• A) 2
• B) 1
• C) 5
• D) 0

Given the following data x:4 5 7 10 y:46 102 294 346 Value of 1st order divided difference f[5 , 7] is

• A) 94
• B) 96
• C) 91
• D) 92

\begin{gathered} For\,the\,giev\,two\,data\,{\text{point}}s\,,\,the\,{\text{degree}}\,of\,Lagrange's\,{\text{interpolation}}\,polynomial\,could\,be \hfill \\ \begin{array}{*{20}{c}} x&{0.3}&{0.7}&{} \\\ y&{0.067}&{0.248}&{} \end{array} \hfill \\\ \end{gathered}

• A) one
• B) two
• C) four
• D) three