Richardson extrapolation method is used to improve the rate of convergence of a …………

• A) Series
• B) Sequence
• C)
• D)

Richardson extrapolation is method also known as …………

• A) Series acceleration method
• B) Sequence acceleration method
• C)
• D)

$\delta \,\, = \,\, - - - -$

• A) ${E^{\frac{1}{2}}}\,\, + \,\,\,{E^{ - \,\,\,\,\frac{1}{2}}}$
• B) $${E^{\frac{1}{2}}}\,\, - \,\,{E^{ - \,\,\,\,\frac{1}{2}}}$$
• C) $\frac{{{E^{\frac{1}{2}}}\,\, + \,\,\,{E^{ - \,\,\,\,\frac{1}{2}}}}}{2}$
• D) None

Zero-th order divided difference is defined as

• A) y[x0]=x0
• B) y[x0]=y1
• C) y[x0]=y0
• D) None of the given choices

In Composite Trapezoidal formula for integrating a Tabular function, we can approximate it with a polynomial whose ---------- order derivative vanishes.

• A) First
• B) Third
• C) Fourth
• D) Second

The step size “h” in numerical integration over the interval [a,b] is defined as

• A) h=(b/a)/n
• B) h=(a-b)/n
• C) h=(b+a)/n
• D) h=(b-a)/n

Geometrically the definite integral of any continuous function f(x) in the interval [a,b] gives ----------.

• A) Volume with dimensions f(x), ‘a’ and ‘b’
• B) Length of segment AB on real line
• C) Area of Trapezoid with dimension of ‘a’ and ‘b’
• D) Area under f(x) on [a,b]

: What will be the value of first order divided difference f[1,5]for the following data x:0 1 5 y:2 1 5

• A) 3
• B) 1
• C) 0
• D) 2

Which of the following method is simplest one to integrate numerically a given tabular function but give more error?

• A) Trapezoidal method
• B) Simpson’s 3/8 Rule
• C) Simpson’s 1/3 Rule
• D) Rectangular method

The double definite integral of a function is called…………

• A) None of the given choices
• B) Length of the curve
• C) Area under the curve
• D) Volume under the curve

$$For\,the\,given\,data\,{\text{points}}\,(4,2.2),\,(8,3.5),\,and\,(12,4.1)\,\,the\,divide\,difference\,table\,will\,be\,given\,as$$

• A) $$\begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 4&{2.2}&{0.325}&{} \\\ 8&{3.5}&{0.15}&{ - 0.0108} \\\ {12}&{4.1}&{}&{} \end{array}$$
• B) $$\begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 4&{2.2}&{0.325}&{} \\\ 8&{3.5}&{0.15}&{ - 0.0219} \\\ {12}&{4.1}&{}&{} \end{array}$$
• C) $$\begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 4&{2.2}&{0.325}&{} \\\ 8&{3.5}&{0.15}&{ - 0.098} \\\ {12}&{4.1}&{}&{} \end{array}$$
• D) $$\begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 4&{2.2}&{0.325}&{} \\\ 8&{3.5}&{0.15}&{ - 0.065} \\\ {12}&{4.1}&{}&{} \end{array}$$

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

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

$$\begin{gathered} What\,will\,be\,the\,value\,of\,'a'\,in\,the\,given\,divide\,difference\,table? \hfill \\ \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D}&{3rdD.D} \\\ 1&{0.4}&{0.25}&{0.0375}&{ - 0.0104} \\\ 3&{0.9}&{0.4}&a&{} \\\ 5&{1.7}&{0.3}&{}&{} \\\ 7&{2.3}&{}&{}&{} \end{array} \hfill \\\ \end{gathered}$$

• A) -0.0012
• B) -0.025
• C) -0.0343
• D) -0.0109

----------- difference is a symmetric function of its arguments.

• A) Backward
• B) None
• C) Forward
• D) Divided

$$For\,the\,given\,data\,{\text{points}}\,(2,0.3),\,(4,1),\,and\,(6,1.2)\,\,the\,divide\,difference\,table\,will\,be\,given\,as$$

• A) $$\begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 2&{0.3}&{0.1}&{} \\\ 4&1&{ - 0.0625}&{0.35} \\\ 6&{1.2}&{}&{} \end{array}$$
• B) $$\begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 2&{0.3}&{ - 0.0625}&{} \\\ 4&1&{0.1}&{0.35} \\\ 6&{1.2}&{}&{} \end{array}$$
• C) $$\begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 2&{0.3}&{0.35}&{} \\\ 4&1&{0.1}&{ - 0.0625} \\\ 6&{1.2}&{}&{} \end{array}$$
• D) $$\begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 2&{0.3}&{ - 0.0625}&{} \\\ 4&1&{0.35}&{0.1} \\\ 6&{1.2}&{}&{} \end{array}$$

At which of the following point the derivatives or slopes the functions f(x) = x – 2 and g(x) = x + 2 may differ?

• A) does not differ for any value of ‘x’
• B) x = -2
• C) x = 2
• D) differ for every value of ‘x’

The percentage error in numerical integration is defined as

• A) = (Theoretical Value-Experiment Value)/ Experiment Value*100
• B) = (Theoretical Value-Experiment Value)* Experiment Value*100
• C) = (Theoretical Value +Experiment Value)/ Experiment Value*100
• D) = (Theoretical Value-Experiment Value)/ Theoretical Value *100

We prefer ………over the Lagrange’s interpolating method for economy of computation.

• A) Newton’s forward difference method
• B) Newton’s backward difference method
• C) Newton’s divided difference method
• D) None of the given choices

Which of the following reason(s) lead towards the numerical integration methods?

• A) All above choices are true
• B) Analytical evaluation of integral is very complicated
• C) Analytical evaluation of integral is impossible
• D) Integrand is given in tabular form

Which of the following is the Richardson’s Extrapolation limit: F3(h/8) provided that F2(h/8) = F2(h/4) = 1 ?

• A) 63
• B) -1
• C) 64
• D) 1