BCA DCA1105 FUNDAMENTALS OF MATHEMATICS

Description

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

 

 

 

 

SET-I

 

 

 

Q1. Let and be two real functions. Find , ,   and .

 

Ans 1.

 

Function Operations

Given:

,

(i)

(ii)

 

 

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Q2. Evaluate the following limits:

 

(i)                                 

 

(ii)  .

 

Ans 2.

(i)

First combine:

Both

 

 

Q3. Find the value of sin 135 and tan⁡15.

Ans 3.

Trigonometric Values

(i)

, and
.

 

 

 

SET-II

 

 

Q4. Decompose into partial fraction.

Ans 4.

Decompose  into partial fractions

Step 1: Check if the fraction is proper

Degree of numerator = 2, degree of denominator = 2 → improper.

So first do

 

Q5. Identify the local maxima and minima for the function using the second derivative test.

Ans 5.

Local maxima and minima of  (second derivative test)

Step 1: First derivative

Critical points:

 

Q6. Evaluate .

Ans 6.

Use the identity:

Here :

So,