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SESSION NOVEMBER 2024 PROGRAM MCA SEMESTER I COURSE CODE & NAME DCA6107 FUNDAMENTALS OF MATHEMATICS Set-I
1. Find the derivative of using limits
Ans 1.
The derivative using limits is defined as:
For :
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2. Evaluate
(i)
Ans 2.
Step 1: Simplify the function
(ii)
Step 1: Expand the function
3. Find and for :
Given function:
Step 1: Partial derivative with respect to ()
Treat as a constant
SET-II
4. Find and where, and .
Ans 4. Find and :
Given vectors:
5. Express 1 Radian into the degree measurement
Ans 5.
To convert radians into degrees, use the formula:
Step 1: Approximate the value of
- Find their modulus and amplitude of the following
(i) (ii).
Ans 6.
Find the modulus and amplitude of the following
(i)
Step 1: Modulus
The modulus of a complex number is given by:
Here, , so and .