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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
- and
- and .
Ans 1.
Composite Functions
(a) Given:
We are asked to find: This
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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:
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
Q6. Determine the value of the following logarithms:
(i) (ii) 1
Ans 6.
(i)
We want to evaluate:
Write 25 as :
Equating