DCA6107 FUNDAMENTALS OF MATHEMATICS JULY AUG 2025

Description

 

SESSION	JULY 2025
PROGRAM	MCA
SEMESTER	I
COURSE CODE & NAME	DCA6107 FUNDAMENTALS OF MATHEMATICS

 

 

SET-I

 

 

 

 

 

 

Question 1:

If , show that

Ans 1.

We know that the derivative of a function  is given by the definition of the limit:

Now, substitute  :

Simplify the numerator using the property  :

 

 

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Its Half solved only

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Question 2.

 

Ans 2.

Let

We split it into three standard integrals:

Question 3. Find all second-order partial derivatives for

Ans 3.

First-order partials

• With respect to :
• With respect to :

 

 

SET-II

 

 

Question 4.

We have to find magnitudes of:
(i)
(ii)
(iii)

Ans 4.

(i) Magnitude of

 

 

Question 5:

Find the value of

(All angles are in degrese:)

Ans 5.

Step 1 – Recall trigonometric values

Angle	aln		tan	500
	1/2	73/2	1/N3	2/43
45″	WV2	1/N2	1
	83/2	1/2	v3	2

 

 

 

Question 6.

Prove that

Ans 6.

Step 1-Square both sides

Square both sides to remove the square root

Step 2 – Multiply numerator and denominator by the conjugate of the denominator Multiply by (  ) to rationalize