Description

SESSION	NOVEMBER 2024
PROGRAM	MCA
SEMESTER	I
COURSE CODE & NAME	DCA6107 FUNDAMENTALS OF MATHEMATICS

 

 

Set-I

 

1. Find the derivative of  using limits

Ans 1.

The derivative using limits is defined as:

For :

Step 1: Rationalize the numerator

Its Half solved only

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2. Evaluate

(i)

Ans 2.

Step 1: Simplify the function

Step 2: Apply the integral

The integral of  is:

 

 

 

(ii)

Step 1: Expand the function

 

 

 

3. Find  and  for :

Given function:

 

Step 1: Partial derivative with respect to  ( )

Treat  as a constant while differentiating with respect to :

Calculation:

1. For :

 

SET-II

 

 

4. Find    and  where ,    and  .

Ans 4. Find  and :

Given vectors:

 

Step 1: Calculate

First, calculate :

 

 

5. Express 1 Radian into the degree measurement

Ans 5.

To convert radians into degrees, use the formula:

 

 

6. Find their modulus and amplitude of the following

(i)                                             (ii).     

Ans 6.

Find the modulus and amplitude of the following

(i)

Step 1: Modulus

The modulus of a complex number  is given by:

Here, , so  and .

Step 2: Amplitude