NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 50  56 of 101
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Question number: 50
» Residues of Complex Function
Appeared in Year: 2009
Describe in Detail
Let C be the contour consisting of the lines, described counterclockwise in the plane. Compute
Explanation
is the contour shown in the figure
To evaluate
Now is a pole of order 1 (simple pole)
Also
… (45 more words) …
Question number: 51
» Taylor Series Expansion (Complex)
Appeared in Year: 2017
Describe in Detail
Let Write down the Taylor Expansion of f in the neighbourhood of .
Explanation
Here
Put
… (94 more words) …
Question number: 52
Appeared in Year: 2015
Describe in Detail
In each of the following cases, state whether the given series is absolutely convergent, conditionally convergent or divergent
a)
b)
c)
Explanation
Option (a) The given series is
Where
Now comparing it with
1)
2
… (170 more words) …
Question number: 53
Appeared in Year: 2006
Question
Pick out series which are absolutely convergent.
Choices
Choice (4)  Response  

a. 


b. 


c. 


d.  Both a. and b. are correct 

Question number: 54
» Sequences and Series (Convergence)
Appeared in Year: 2005
Describe in Detail
What are the value of for which the following series is convergent?
Explanation
Let the omen series be denoted by ……. . eq. (1)
Where
Since for absolute convergence, we take
Now is convergent if …………eq. (2)
… (94 more words) …
Question number: 55
» Order of Pole and Its Residue
Appeared in Year: 2010
Describe in Detail
Find the order of the pole and its residue at of the function
Explanation
Order of pole
… (119 more words) …
Question number: 56
» Line Integral in Complex Plane
Appeared in Year: 2017
Describe in Detail
Let C be the contour in the complex plane consisting of two straight line segments, one from and the other from . Evaluate
Where
Explanation
Along OM
The imaginary axis from is the line segment
Now on so that
Also y varies from
… (103 more words) …