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

The percentage error in numerical integration is defined as
= (Theoretical ValueExperiment Value)* Experiment Value*100
= (Theoretical Value +Experiment Value)/ Experiment Value*100
= (Theoretical ValueExperiment Value)/ Theoretical Value *100
Theoretical ValueExperiment 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
Y(xi+H)y(xih)/2h
Y(xi+H)y(xih)/2^h
Y(xi+H)+y(xih)/2^h
Trapezoidal rule of integration of a definite integral is of?
o(h2)
none of the given choice
Top of Form
One
Two
Three
None of given option
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 1^{st} derivative at x=1 by using two point formula ? =((1)/(1+0.01))+((1)/(10.01))/ =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)
(y2y4)/2
(y2y4)
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= [ba]/n
h= [b+a]/n
h= [ab]/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 subintervals. 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 NewtonCotes 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
Differences methods find the ________ solution of the system.
Select correct option:
numerical
Analytical
Question # 6 of 10 ( Start time: 10:26:49 AM ) Total Marks: 1
The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power.
Select correct option:
(x1)^3
(x+1)^3 i m not sure about this answer
x^31
x^3+1
Question # 7 of 10 ( Start time: 10:28:08 AM ) Total Marks: 1
The Power method can be used only to find the eigen value of A that is largest in absolute value—we call this eigen value the dominant eigen value of A.
Select correct option:
TRUE
FALSE
Question # 8 of 10 ( Start time: 10:29:33 AM ) Total Marks: 1
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.
Select correct option:
main diagonal
last column
last row
first row i m not sure about this answer
Question # 9 of 10 ( Start time: 10:30:33 AM ) Total Marks: 1
If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.
Select correct option:
TRUE
FALSE
Question # 10 of 10 ( Start time: 10:31:28 AM ) Total Marks: 1
Sponsored LinksA 3 x 3 identity matrix have three and different eigen values.
Select correct option:
TRUE
FALSE
MTH603 Numerical Analysis QUIZ No.2
Exact solution of 2/3 is not exists.
TRUE
FALSE
The Jacobi’s method is
a method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.
no
atleast one
A 3 x 3 identity matrix have three and __________eigen values.
same
different
Eigenvalues of a symmetric matrix are all _______ .
real
complex
zero
positive
The Jacobi iteration converges, if A is strictly diagonally dominant.
TRUE
FALSE
Below are all the finite difference methods EXCEPT _________.
jacobi’s method
newton's backward difference method
Stirlling formula
Forward difference method
If n x n matrices A and B are similar, then they have the same eigenvalues (with the same multiplicities).
TRUE
FALSE
If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.
TRUE
FALSE
The characteristics polynomial of a 3x 3
identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power.
(x1)^3
(x+1)^3
x^31
x^3+1
Two matrices with the same characteristic polynomial need not be similar.
TRUE
FALSE
Question # 1 of 10 ( Start time: 10:22:24 AM ) Total Marks: 1
Eigenvalues of a symmetric matrix are all _________.
Select correct option:
real
zero
positive
negative
Question # 2 of 10 ( Start time: 10:23:07 AM ) Total Marks: 1
An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.
Select correct option:
TRUE
FALSE
Question # 3 of 10 ( Start time: 10:23:55 AM ) Total Marks: 1
Exact solution of 2/3 is not exists.
Select correct option:
TRUE
FALSE
Question # 4 of 10 ( Start time: 10:24:53 AM ) Total Marks: 1
The GaussSeidel method is applicable to strictly diagonally dominant or symmetric ________ definite matrices A.
Select correct option:
positive
negative
Question # 5 of 10 ( Start time: 10:26:04 AM ) Total Marks: 1
Differences methods find the ________ solution of the system.
Select correct option:
numerical
Analytical
Question # 6 of 10 ( Start time: 10:26:49 AM ) Total Marks: 1
The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power.
Select correct option:
(x1)^3
(x+1)^3 i m not sure about this answer
x^31
x^3+1
Question # 7 of 10 ( Start time: 10:28:08 AM ) Total Marks: 1
The Power method can be used only to find the eigenvalue of A that is largest in absolute value—we call this eigenvalue the dominant eigenvalue of A.
Select correct option:
TRUE
FALSE
Question # 8 of 10 ( Start time: 10:29:33 AM ) Total Marks: 1
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.
Select correct option:
main diagonal
last column
last row
first row i m not sure about this answer
Question # 9 of 10 ( Start time: 10:30:33 AM ) Total Marks: 1
If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.
Select correct option:
TRUE
FALSE
Question # 10 of 10 ( Start time: 10:31:28 AM ) Total Marks: 1
A 3 x 3 identity matrix have three and different eigen values.
Select correct option:
TRUE
FALSE
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