Two-point formula for the first derivative is defined as

• A) y(xi+h)+y(xi-h)/h^2
• B) y(xi+h)-y(xi-h)/h^2
• C) y(xi+h)+y(xi-h)/2h
• D) y(xi+h)-y(xi-h)/2h

In Trapezoidal rule, we assume that f(x) is continuous on [a, b] and we divide [a, b] into n subintervals of equal length using the ………points.

• A) None of the given choices
• B) n
• C) n-1
• D) n+1

Three-point formula for the second derivative is defined as

• A) y(xi+h)-2y(xi)+y(xi-h)/h^2
• B) y(xi+h)+2y(xi)+y(xi-h)/h^2
• C) y(xi+h)-2y(xi)+y(xi-h)/2h
• D) y(xi+h)-2y(xi)-y(xi-h)/h^2

If the given tabular function f(x) is approximated by the polynomial ‘P1(x) = x+1’ then which of the following polynomial will approximate the derivative of f(x) ?

• A) x-1
• B) 1
• C) 2x
• D) x

Which of the following is the Richardson’s Extrapolation limit: F1(h/2) provided that F(h/2) = F(h) = 1 ?

• A) 3
• B) 1
• C) 4
• D) 0

The area of a trapezoid is obtained by adding the area of a …………and a triangle.

• A) Circle
• B) None of the given choices
• C) Rectangle
• D) Square

For a function ‘f(x) = x’, with a step size of ‘h=0.01’, which of the following gives the 1st derivative at x =1 by using two point formula?

• A) y’(x) = 1+Some Truncation Error
• B) y’(x) = 1.01 + Some Truncation Error
• C) y’(x) = -0.1 + Some Truncation Error
• D) y’(x) = 0.1 + Some Truncation Error

Differential operator in terms of forward difference operator is given by

• A) $$D = \frac{1}{h}(\Delta - \frac{{{\Delta ^2}}}{{2!}} + \frac{{{\Delta ^3}}}{{3!}} - \frac{{{\Delta ^4}}}{{4!}} + \frac{{{\Delta ^5}}}{{5!}} - ...)$$
• B) $$D = \frac{1}{h}(\Delta + \frac{{{\Delta ^2}}}{2} + \frac{{{\Delta ^3}}}{3} + \frac{{{\Delta ^4}}}{4} + \frac{{{\Delta ^5}}}{5} + ...)$$
• C) $$D = \frac{1}{h}(\Delta - \frac{{{\Delta ^2}}}{2} + \frac{{{\Delta ^3}}}{3} - \frac{{{\Delta ^4}}}{4} + \frac{{{\Delta ^5}}}{5} - ...)$$
• D) $$D = \frac{1}{h}(\Delta + \frac{{{\Delta ^2}}}{{2!}} + \frac{{{\Delta ^3}}}{{3!}} + \frac{{{\Delta ^4}}}{{4!}} + \frac{{{\Delta ^5}}}{{5!}} + ...)$$

In Richardson’s extrapolation method, we usually use two different step sizes ………and …… to yield a higher order method.

• A) h/2,h/4
• B) h,h/2
• C) h/2,h/3
• D) None of the given choices

Given the following data x:0 1 4 y:2 1 4 Value of first order divided difference y[0,1]is

• A) 2
• B) -1
• C) 1
• D) -2

While using the Composite Trapezoidal form for integrating y = f(x) in [0,10] which is subdivided in equally spaced interval of width ‘h =2’, then which of the following is the area of associated trapezoidal strip over subinterval:[2,4] ?

• A) (y2 – y4)/2
• B) (y2 – y4)
• C) (y2 + y4)
• D) (y2 + y4)/2

To improve the accuracy of the derivative of the function, which of the following method is more helpful?

• A) Divided Difference
• B) Interpolation
• C) Central Difference
• D) Extrapolation

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

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

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

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

1st ordered divided difference formula is defined as

• A) y[x0,x1]=(y1+y0)/(x1-x0)
• B) None of the given choices
• C) y[x0,x1]=(y1-y0)/(x1+x0)
• D) y[x0,x1]=(y1-y0)/(x1-x0)

To take the derivative of f(x) = 2x in the interval [-3,3], which of the following partition of subintervals will be suitable?

• A) Unequally spaced
• B) Equally spaced
• C) Any arbitrary partition will work
• D) Union of equally spaced and unequally spaced intervals.

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

• A) 4th
• B) 5th
• C) 2nd
• D) 3rd

$$\begin{gathered} What\,will\,be\,the\,value\,of\,'a'\,in\,the\,given\,divide\,difference\,table? \hfill \\ \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 3&{0.4}&{}&{} \\\ 6&{0.9}&{0.1667}&{} \\\ 9&{1.7}&{0.2667}&a \end{array} \hfill \\\ \end{gathered}$$

• A) 0.0254
• B) 0.0349
• C) 0.0211
• D) 0.0167

Integration is a ………………process.

• A) None of the given choices
• B) Subtracting
• C) Summing
• D) Dividing

Geometrically, in Simpson’s 1/3 Rule, we find the area of -------- strip/strips at time under a curve of given function.

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