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Description
SESSION | November 2024 |
PROGRAM | Bachelor of COMPUTER APPLICATIONS (BCA) |
SEMESTER | I |
course CODE & NAME | Fundamentals of Mathematics (DCA1105) |
SET-I
- Show that the relation R in the set given by is reflexive but neither symmetric nor transitive.
Ans 1.
To analyze the relation on the set defined by , we will examine its properties: reflexivity, symmetry, and transitivity.
Reflexivity
A relation on a set is reflexive if every element of is related to itself, i.e., for all .
In this case, , and we observe that:
- (element is related to itself),
- (element is related
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- Write the composite function if
- and
- and .
Ans 2.
To find the composite function , we substitute the function into . Let’s compute the composite functions for each pair of and :
(a) Given and :
To compute , substitute into :
- Evaluate the followings:
(i) (ii)
Ans 3.
(i)
Step 1: Identify the dominant terms
As , the dominant term in the numerator and denominator is . To simplify, divide every term in the numerator and
SET-II
- Find the derivative of .
Ans 4.
To find the derivative of
we use the quotient rule:
- Consider the function . Determine where the function is increasing or decreasing.
Ans 5.
Determine where is increasing or decreasing
To determine where is increasing or decreasing, follow these steps:
Step 1: Find the
- Evaluate (i)
(ii)
Ans 6.
(i)
Use integration by parts: , where:
- Let , so