MTH603 Final Term MCQs Unsolved and Solved

Mth603 Just Final term MCQS

(latest quiz included and FAQs and Glossary is also included in this file) Plz must learn the FAQs and Glossary for Mcqs and short question.. It is very helpful By

Tayyaba Rehmna MCS 4th semester

File made on 25-july-2013

If we wanted to find the value of a definite integral with an infinite limit, we can instead replace the infinite limit with a variable, and then take the limit as this variable goes to

Constant Finite

Infinity

zero

In Runge – Kutta Method, we do not need to calculate higher order derivatives and find greater accuracy.

True

False

O(h2) O(h3) O(h4) None of given

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 i m not sure about this answer

x^3-1 x^3+1 In Richardson’s extrapolation method, we usually use two different step sizes ………and …… to yield a higher order method.

h, h/2

h, h/3 h, h/4 None In Simpson’s 3/8 rule, we divide the interval of integration into n sub-intervals. Where n is divisible by.....

None Euler's method is only useful for a few steps and small step sizes; however Euler's method together with Richardson extrapolation may be used to increase the

order and accuracy

divergence

The first lngrange polynomial with equally spaced nodes produced the formula for

Trapezoidal rule

Newton's method Richardson's method

The need of numerical integration arises for evaluating the indefinite integral of a function that has no explicit antiderivative or whose antiderivative is not easy to obtain. TRUE

FALSE

The Trapezoidal Rule is an improvement over using rectangles because we have much less "missing" from our calculations. We used ________ to model the curve in trapezoidal Rule

straight lines

curves parabolas constant

The Euler method is numerically unstable because of ________ convergence of error. Slow Fast Moderate No Adams – Bashforth is a multistep method.

True

False

1. The relationship between central difference operator and the shift operator is given by
2. In Simpson’s 3/8 rule,

f x

is of the form

1. ax

b

ax bx c

ax bx cx d

ax bx cx dx e

3. In Trapezoidal rule, the integral is computed on each of the sub-intervals by using linear interpolating formula, ie. For n=1 and then summing them up to obtain the desired integral.

•  True
•  False

4. If f (x) contains trigonometric, exponential or logarithmic functions then this equation is known as Transcendental equation Algebraic Polynomial Linear

The step size “h” in numerical integration over the interval [a,b] is defined as h=(b-a)/n

ok(page 227)

The single definite integral of a function is called

Area under the curve

ok(page 176)

Integration is a ………………process. Summing

ok(page 170)

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

(page 185)

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 or Simpson‟s rule, repeatedly with respect to ………variable at a time. One

ok(page 185)

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

(page 252)

In Simpson‟s rule, we can estimate the integral by …………the areas under the parabolic arcs through three successive points. Adding

ok

on.pdf)

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?

Trigonometric Function Exponential Function Logarithmic Function

Polynomial Function

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 ?

-1

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

Independent

Arbitrary 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

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

Four

None of the given choices

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

Richardson’s extrapolation method

None of the given choices 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

O(h2) O(h3)

O(h4)

None of the given choices

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?

ok

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

ok(h=b-a/n) · Midterm Objective MTH603 · Solved 100% correct · MCS 4th semester.