NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 26 - 34 of 101
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Question number: 26
Appeared in Year: 2013
Write in Short
Find the points where the function is continous
Question number: 27
Appeared in Year: 2006
Write in Short
Evaluate
Question number: 28
» Differentiability in Complex Plane
Appeared in Year: 2011
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 –
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Question number: 29
Appeared in Year: 2017
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
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Question number: 30
» Taylor Series Expansion (Complex)
Appeared in Year: 2015
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
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Question number: 31
Appeared in Year: 2005
Describe in Detail
What is the Radius of Convergence of the power series
?
Explanation
The given power series is
Now
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Question number: 32
» Leibniz Rule for Differentiation under Integral Sign
Appeared in Year: 2006
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
Appeared in Year: 2010
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
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Question number: 34
Appeared in Year: 2008
Write in Short
Evaluate: