DCA1105 FUNDAMENTALS OF MATHEMATICS APRIL 2025

Description

 

SESSION	APRIL 2025
PROGRAM	Bachelor of CoMPUTER APPLICATIONS (BCA)
SEMESTER	I
course CODE & NAME	DCA1105 Fundamentals of Mathematics

 

 

                                                     SET-I

 

 

 

 

Q1. Write the composite function  if

1. and  
2. and   .

 

Ans 1.

Composite Functions

(a) Given:

We are asked to find:  This means substitute  into .

Solution:

Now expand:

Ans:

Its Half solved only

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Q2. Evaluate the followings:

(i)                (ii)  

Ans 2.

Limits

(i)

Evaluate:

Step-by-step:

• Identify the highest power of in both numerator and denominator:
• Divide numerator and denominator by

 

 

 

 

Q3. Find the value of  and .

Ans 3.

 (a)

We can write:

Use identity:

Let , :

 

 

 

 

SET-II

 

 

Q4. Decompose into partial fraction.

 

Ans 4.

Decompose into Partial Fractions:

Given:

We want to write:

Step 1: Combine the RHS

 

 

 

Q5. Consider the function . Determine where the function is increasing or decreasing.

Ans 5.

Determine where the function is increasing or decreasing

Given function:

Step 1: Find the first derivative

To determine where the function is increasing or decreasing, we use the first derivative test:

 

 

 

Q6. Determine the value of the following logarithms:

   (i)                        (ii)  1

Ans 6.

(i)

We want to evaluate:

Write 25 as :