by Rahul Anand | May 9, 2023 | CALCULUS
Derivative of \( cosθ \) using the First Principle Let \(y\) = \( cosθ \) ∴ \(y + δy\) = \( cos(θ + δθ) \) ∴ \(δy\) = \( cos(θ + δθ) \) – \( cosθ \)From Trigonometry , we have \( cos(A-B) \) = -2.\( sin \dfrac {(A+B)}{2} \).\( sin \dfrac {(A-B)}{2} \)Using the...
by Rahul Anand | May 8, 2023 | SETS
De Morgan’s First Law The complement of the union of two sets is equal to the intersection of their complements i.e. (A ∪ B )’ = A’ ∩ B’ De Morgan’s Second Law The complement of the intersection of two sets is equal to the union of their complements...
by Rahul Anand | May 8, 2023 | SETS
A cartesian product between two sets is defined as the set consisting of all possible ordered pairs that can be formed by taking one element from each of the sets at a given time. If A and B are two sets such that a ∈ A and b ∈ B, then the cartesian product between A...
by Rahul Anand | May 8, 2023 | RELATIONS & FUNCTIONS
In mathematics, a tuple or a sequence is a list of objects arranged in an order. Such a list may have repeated objects but the order is more important. Such sequences or tuples are denoted as ( t1, t2, t3, …., tn ) where tn is the nth element of the list. Below are a...
by Rahul Anand | May 8, 2023 | SETS
An ordered pair is a 2-tuple formed by taking two elements (generally numbers but can be alphabets, characters, words, or symbols). The general form of representation is (a, b) where a and b represent two distinct objects. The important thing with ordered pairs is...
by Rahul Anand | May 8, 2023 | SETS
The cartesian product of two sets A and B is defined as a set formed by all the possible ordered pairs of elements from A and B, such that the first element comes from set A and the second element comes from set B. The cartesian product is denoted as A × B....
