NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 8 - 13 of 101

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Question number: 8

» Exponential Series

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Appeared in Year: 2013

Essay Question▾

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

» Cauchy-Riemann Equation.

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Appeared in Year: 2005

Short Answer Question▾

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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

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Appeared in Year: 2006

Essay Question▾

Describe in Detail

Evaluate

Explanation

It is of the form where

Replace

Lower limit

Lower limit

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Question number: 11

» Indeterminate Forms

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Appeared in Year: 2006

Short Answer Question▾

Write in Short

Evaluate

Question number: 12

» Convergence of Positive Series Test

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Appeared in Year: 2013

MCQ▾

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

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Appeared in Year: 2012

Essay Question▾

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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