NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 8  13 of 101
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Question number: 8
Appeared in Year: 2013
Describe in Detail
Let. Find the sum of the infinite series.
Explanation
Let
Put
…………… eq. (A)
Now we know the exponential series
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Question number: 9
Appeared in Year: 2005
Write in Short
Let be two twice continuously differentiable functions on satisfying the Cauchy –Riemann equation. Let. Define. Express the complex derivative of i. e. in terms of the partial derivatives of .
Question number: 10
» Definite Integral as Limit of a Sum
Appeared in Year: 2006
Describe in Detail
Evaluate
Explanation
It is of the form where
Replace
Lower limit
Lower limit
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Question number: 11
Appeared in Year: 2006
Write in Short
Evaluate
Question number: 12
» Convergence of Positive Series Test
Appeared in Year: 2013
Question
Which of the following series are convergent?
Choices
Choice (4)  Response  

a. 


b. 


c. 


d.  Both a. and b. are correct 

Question number: 13
» Differentiability in Complex Plane
Appeared in Year: 2012
Describe in Detail
Define
Which of the following statements are true?
a) is not differentiable at
b) is differentiable at
c) is differentiable only at
Explanation
Using the Result
If
Then is continous at i. e if is root of , then is continous at and these are the only points at which fun
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