NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 26 - 34 of 101

Access detailed explanations (illustrated with images and videos) to 101 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. Unlimited Access for Unlimited Time! View Sample Explanation or View Features.

Rs. 300.00 or

How to register?

Question number: 26

» Continuity

Edit

Appeared in Year: 2013

Short Answer Question▾

Write in Short

Find the points where the function is continous

Question number: 27

» Cauchy Residue Theorem

Edit

Appeared in Year: 2006

Short Answer Question▾

Write in Short

Evaluate

Question number: 28

» Differentiability in Complex Plane

Edit

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Find the points z in the complex plane where exists and evaluate it at those points

a)

b) , Where denotes the imaginary part of z.

Explanation

(a) Let

Clearly all the four partial derivatives exist and continuous functions of

The points z in the complex plane where exist are those for which Cauchy –

… (317 more words) …

Question number: 29

» Binomial Series

Edit

Appeared in Year: 2017

Essay Question▾

Describe in Detail

Let , be a fixed positive integer. Let for

Evaluate:

Explanation

Numerical value of last term of

i. e

And

Here

The given series is

Differentiating both sides with respect to , we get

… (252 more words) …

Question number: 30

» Taylor Series Expansion (Complex)

Edit

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Write down the power series expansion of the function in a neighbourhood of .

Explanation

So that

This is the Required power series Expansion of the func

… (16 more words) …

Question number: 31

» Radius of Convergence

Edit

Appeared in Year: 2005

Essay Question▾

Describe in Detail

What is the Radius of Convergence of the power series

?

Explanation

The given power series is

Now

… (6 more words) …

Question number: 32

» Leibniz Rule for Differentiation under Integral Sign

Edit

Appeared in Year: 2006

Essay Question▾

Describe in Detail

Let . Define Evaluate as a function of x.

Explanation

Leibnitz Rule is given by

If the function are defined on and are differentiation at a point is continuous, then

… (171 more words) …

Question number: 33

» Cauchy Residue Theorem

Edit

Appeared in Year: 2010

Essay Question▾

Describe in Detail

Let C denote the circle in the complex plane, described in the positive i. e (anti-clockwise) sense. Evaluate

Explanation

Here let

Here is a simple pole and lies within the circle

By Cauchy residue theorem

… (22 more words) …

Question number: 34

» Trigonometric Identities

Edit

Appeared in Year: 2008

Short Answer Question▾

Write in Short

Evaluate:

Developed by: