dy/dx - = 1 - y,y(0) = 0 is an example of

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Question # 7 of 10 ( Start time: 09:16:40 PM ) Total Marks: 1

In Romberg’s method, accuracy of Simpson and Trapezoidal rules is improved by ---------.
Select correct option:
interpolation
extrapolation

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Question # 8 of 10 ( Start time: 09:18:38 PM ) Total Marks: 1

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

Select correct option:
Newton’s forward difference method
Newton’s backward difference method
Newton’s divided difference method
None of the given choices

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Question # 9 of 10 ( Start time: 09:17:41 PM ) Total Marks: 1

Richardson extrapolation is method also known as …………

Select correct option:
Sequence acceleration method
Series acceleration method

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Question # 10 of 10 ( Start time: 09:18:38 PM ) Total Marks: 1

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

Select correct option:
At x=1
At x=2
At x=3
At x=4

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Question # 1 of 10 ( Start time: 09:28:45 PM ) Total Marks: 1

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

Select correct option:
Newton’s forward difference method
Newton’s backward difference method
Newton’s divided difference method
None of the given choices

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1st ordered divided difference formula is defined as

Select correct option:
y[x0,x1]y1+y0)/(x1-x0)
y[x0,x1]y1-y0)/(x1+x0)
y[x0,x1]y1-y0)/(x1-x0)
None of the given choices

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

Select correct option:
Length of segment AB on real line
Volume with dimensions f(x), ‘a’ and ‘b’
Area under f(x) on [a,b]
Area of Trapezoid with dimension of ‘a’ and ‘b’

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

Select correct option:
Trapezoidal Method
Simpson’s 1/3 Rule
Simpson’s 3/8 Rule
Romberg’s Method

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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.

Select correct option:
Odd
**Even **
Prime
None of the given choices

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

Select correct option:
differ for every value of ‘x’
does not differ for any value of ‘x’
x = 2
x = -2

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

Select correct option:
3/2
-3/2
1/2
-1/2

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Simpson’s 3/8 rule represents the area between the curve y = f(x) in the interval say [a,b] above x-axis by approximating the given curve by the ----------.

Select correct option:
Cubic curve through one point
Cubic curve through two points
Cubic curve through three points
Cubic curve through four points

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Zero-th order divided difference is defined as

Select correct option:
y[x0]=x0
y[x0]=y1
y[x0]=y0
None of the given choices

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Which of the following is the Global Error for Simpson’s 3/8 Rule while integrating ‘f(x) = Cosx’ in the interval of [0,pi] of equally spaced subinterval of width ‘h =pi/6’and intermediate point x = pi/2?

Select correct option:
-pi/80
pi/800
0
1

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

Select correct option:
0.2
0.4
2
-2

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

Select correct option:
0.2
0.4
2
-2