MTH603 quiz 3 !!!

[waseem gul]

please upload quizz 3 if nay one attempt!! hurry up  

[waseem gul]

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

[waseem gul]

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 1^st 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

 

 

 

 

[Smile, Its Sunnah :)]

   
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

[+ M.Tariq Malik]

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+1)^3 i m not sure about this answer

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

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

[+ M.Tariq Malik]

MTH603 Numerical Analysis QUIZ No.2 

mth6032ndquizz29112012.docx

[+ M.Tariq Malik]

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+1)^3 i m not sure about this answer
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
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

[+ M.Tariq Malik]

mth603 quiz 1 solved 2020

mth603 final term solved papers by moaaz

mth603 solved mcqs

mth603 quiz 1 2020

mth603 quiz no 01

mth603 midterm solved papers

mth603 quiz spring 2020

mth 603 solved quiz