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Replies to This Discussion

1_Trapezoidal rule of integration of a definite integral is of…………

O(h2)
 
2_Simpson’s 1/3 rule is based on fitting three points with a ………………
Quadratic
3_Simpson’s 3/8 rule is based on fitting ……………… points by a cubic.
Four
 
4_1st ordered divided difference formula is defined as
y[x0,x1]=(y1+y0)/(x1-x0)
 
5_To take the derivative of f(x) = 2x in the interval [-3,3], which of the following partition of subintervals will be suitable?
Equally spaced
 
6_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
single
 
7_At which of the following points the Maximum value of 2nd derivative of function f(x) = -(2/x) in the interval:[1,4] exits?
At x=1
 
8_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] ?
(y2 + y4)/2
 
9_The area of a trapezoid is obtained by adding the area of a …………and a triangle.
Rectangle
 
10_In Richardson’s extrapolation method, we usually use two different step sizes ………and …… to yield a higher order method.
h,h/2



In Newton-Cotes formula for finding the definite integral of a tabular function, which of the following is taken as an approximate function then find the desired integral?

Select correct option:

Trigonometric Function

Exponential Function

Logarithmic Function

Polynomial Function 166

 

If the area under ‘f(x) = x’ in interval [0,2] is subdivided into two equal sub-intervals of width ‘1’ with left end points, then which of the following will be the Truncation Error provided that I(definite integral) = 2 and approximate sum = 3 ?

Select correct option:

0

1

-1

3

 

Trapezoidal and Simpson’s integrations are just a linear combination of values of the given function at different values of the …………variable.

Dependent

Independent 179

Arbitrary 

None of the given choices

 

Simpson’s 3/8 rule is based on fitting ……………… points by a cubic. 

Two

Three

Four 169

None

 

We can improve the accuracy of trapezoidal and Simpson’s rules using ……

Simpson’s 1/3 rule

Simpson’s 3/8 rule

Richardson’s extrapolation method 178

None of the given choices

 

 

In Simpson’s 1/3 rule, the global error is of ……………… 

O(h2)

O(h3)

O(h4) 171

None of the given choices

The percentage error in numerical integration is defined as 

= (Theoretical Value-Experiment Value)* Experiment Value*100

= (Theoretical Value +Experiment Value)/ Experiment Value*100

= (Theoretical Value-Experiment Value)/ Theoretical Value *100

Theoretical Value-Experiment Value)/ Experiment Value*100

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

actual function

extrapolating polynomial

Lagrange’s polynomial

Newton’s Divided Difference Interpolating polynomial


  • Q; Two-point formula for the first derivative is defined as
          Y(xi+H)-y(xi-h)/2h

Y(xi+H)-y(xi-h)/2h

Y(xi+H)-y(xi-h)/2^h

Y(xi+H)+y(xi-h)/2^h

 

 

Trapezoidal rule of integration of a definite integral is of?
o(h2)

 

  • o(h3)
  • o(h4)

none of the given choice

 

 

Top of Form

 

 

  • Q; To evaluate numerically a double integral over a rectangular region bounded by the lines x=a, x=b, y=c, y=d we shall employ either trapezoidal rule of Simpson’s rule, repeatedly with respect to ||| variable at a time

 

One

Two

Three

None of given option

 

 

 

 

  • Q: Which of the following is the cote’s number ( weighting coefficient) of the function: f(x)=x+1 in the interval [0,1]?
    3/2

-3/2

½

-1/2

 

For a function f’(x)=x’ with a step size of h’ = 0.01’ , which if the following gives the 1st derivative at x=1 by using two point formula ? =-((1)/(1+0.01))+((1)/(1-0.01))/ =2*0.01=1.0001

Y’=(x)=1+Some truncation Error

Y’=(x)=1.01+Some truncation Error

Y’=(x)=.0.1+Some truncation Error

Y’=(x)=0.1+Some truncation Error

 

 

 

Top of Form

 

While employing trapezoidal and Simpson rules to evaluate the double integral numerically, by using trapezoidal and Simpson rule over …….

Plane region

Real line

 

 

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

linr

Quadratic polynomial

Cubic

None of the given choice

 

 

Q: 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
Single

Both

 

 

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.
odd

Even.

Prime

None of given option

 

 

Bottom of Form

 

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

 

(y2+y4)/2

(y2+y4)

(y2|y4)/2

(y2|y4)

 

 

 

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

 

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

63

64

1

-1

 

 

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

h= [b-a]/n

h= [b+a]/n

h= [a-b]/n

h= [b/a]/n

 

 

 

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

Rectangular method

Simpson’s 1/3 rule

Simpson’s 3/8 rule

 

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’= 6’ and intermediate point x = pi/2?

-pi / 80

Pi/80

0

1

 

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


Extrapolation.

Interpolation

Divided difference

Central difference

 

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

Rectangle

Square

Circle

Non of given

 

In Simpson’s 3/8 rule, we divide the interval of integration into n sub-intervals. Where n is divisible by…
3

2

4

None of given

 


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

 

 

 

 

   
Question # 1 of 10 ( Start time: 11:27:53 PM )     Total

Marks: 1
In the process of Numerical Differentiation, we

differentiate an interpolating polynomial in place of

------------.

Select correct option:
    actual function
    extrapolating polynomial
    Lagrange’s polynomial
    Newton’s Divided Difference Interpolating

polynomial


Question # 2 of 10 ( Start time: 11:28:11 PM )     Total

Marks: 1
In Newton-Cotes formula for finding the definite

integral of a tabular function, which of the following

is taken as an approximate function then find the

desired integral?
Select correct option:
    Trigonometric Function
    Exponential Function
    Logarithmic Function
    Polynomial Function



Question # 3 of 10 ( Start time: 11:29:01 PM )     Total

Marks: 1
Simpson’s 1/3 rule is based on fitting three points with

a ………………
Select correct option:
    Cubic
    Quadratic


Question # 4 of 10 ( Start time: 11:29:14 PM )     Total

Marks: 1
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


Question # 5 of 10 ( Start time: 11:29:42 PM )     Total

Marks: 1
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

     
Question # 6 of 10 ( Start time: 11:30:58 PM )     Total

Marks: 1
In double integration, we keep one variable say x fixed

and ……………
Select correct option:
    Reliable the other variable y
    Varying the other variable y


Question # 7 of 10 ( Start time: 11:31:25 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


Question # 8 of 10 ( Start time: 11:31:49 PM )     Total

Marks: 1
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


Question # 9 of 10 ( Start time: 11:32:07 PM )     Total

Marks: 1
The idea of Richardson’s extrapolation is to combine two

computed values of derivative of y using the same method

but with ……… different step sizes.
Select correct option:
    Two
    Three
    Four
    None of the given choices


Question # 10 of 10 ( Start time: 11:32:37 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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