NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 89 - 96 of 101

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Question number: 89

» Definite Integral

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Appeared in Year: 2010

Essay Question▾

Describe in Detail

Let be continuously differentiable.

Evaluate

Explanation

It is of the form

So using

Function is continuously differentiable)

Question number: 90

» LMVT

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Appeared in Year: 2012

MCQ▾

Question

Pick out the true statements:

Choices

Choice (4)Response

a.

for all

b.

for all

c.

for all

d.

All of the above

Question number: 91

» Definite Integral

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Appeared in Year: 2016

Essay Question▾

Describe in Detail

Evaluate

Explanation

Graph of the points of intersection

Graph of the Points of Intersection

Drow the graphs of .

Their points of intersection are given by

The region in the dark is the

… (89 more words) …

Question number: 92

» Leibniz Rule for Successive Differentiation

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Appeared in Year: 2012

Essay Question▾

Describe in Detail

Write down explicitly the Expression for the nth derivative of the function.

Explanation

If are function of x possessing nth derivative then

[Leibnitz Theorem]

Let

.

.

By Leibnitz Theorem

… (153 more words) …

Question number: 93

» Line Integral in Complex Plane

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Appeared in Year: 2012

Essay Question▾

Describe in Detail

Let be the Boundary of the square in the complex plane with vertices at the points which is described in the anticlockwise direction. Evaluate .

Explanation

The boundary of the square

The Boundary of the Square

Along OA

…………. eq. (1)

Along AB

… (380 more words) …

Question number: 94

» Cauchy Residue Theorem

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Appeared in Year: 2008

Short Answer Question▾

Write in Short

Let be a simple closed contour in the complex plane described in the positive sense. Evaluate.

When

a) lies inside and

b) lies outside

Question number: 95

» Points of Continuity

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Appeared in Year: 2013

Essay Question▾

Describe in Detail

In each of the following find the points of continuity of f.

a)

b)

Explanation

Option (a) is discontinuous for all values of x on real line

Points of continuity

Option (b) is continous when

… (362 more words) …

Question number: 96

» Inequalities Using LMVT

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Appeared in Year: 2012

Essay Question▾

Describe in Detail

Let . Fill in the blanks with the correct sign :

a) ________

b) ________

Explanation

(a) Let

Then satisfies the conditions of LMVT in consequently there exists some satisfying such that

………………eq. (A)

… (250 more words) …

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