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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 ………………
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

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.

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

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

## MTH603 - Numerical Analysis Online Quiz No

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:

(x-1)^3

x^3-1

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

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

mth6032ndquizz29112012.docx

## mth603 solved mcq's

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.

(x-1)^3
(x+1)^3
x^3-1
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 Gauss-Seidel 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:

(x-1)^3
x^3-1
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

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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