NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 89  95 of 101
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Question number: 89
Appeared in Year: 2010
Describe in Detail
Let be continuously differentiable.
Evaluate
Explanation
It is of the form
So using
Function is co
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Question number: 90
» LMVT
Appeared in Year: 2012
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
Appeared in Year: 2016
Describe in Detail
Evaluate
Explanation
Drow the graphs of .
Their points of intersection are given by
The region in the dark is the
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Question number: 92
» Leibniz Rule for Successive Differentiation
Appeared in Year: 2012
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
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Question number: 93
» Line Integral in Complex Plane
Appeared in Year: 2012
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
Along OA
…………. eq. (1)
Along AB
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Question number: 94
Appeared in Year: 2008
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
Appeared in Year: 2013
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
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