Multiplication and division property
The following are also true. where a is a non-zero constant. ..
The following are also true. where a is a non-zero constant. ..Expansions
In algebra we come across certain products very frequently. For e.g., (a + b) 2 , (a + b) 3 (a + b + c) 2 etc. These are nothing but products of binomials or trinomials. We derive the formulae for these products and apply them whenever necessary. These expansions help us to avoid elab..
Introduction
An equation of the form ax 2 +bx+c=0 where a, b, c are real numbers and where "a" does not equal to zero(0..
One-one function (or an injective map)
A function f : A g B is called a 1-1 mapping, if every element of f(A) does not have more than one pre-image. ..
A function f : A g B is called a 1-1 mapping, if every element of f(A) does not have more than one pre-image. ..Limits (Contd....)
Limits at infinity: If x is a variable such that it can take any real value how much ever The two important properties of these one-sided limits that i) If the left hand limit and right hand limit of a function at a point exists, but are not equal, then we conclude that the limit..
Limits at infinity: If x is a variable such that it can take any real value how much ever The two important properties of these one-sided limits that i) If the left hand limit and right hand limit of a function at a point exists, but are not equal, then we conclude that the limit..Summary of Relation properties
: If aRb then bRa. Let a be brother of b then b may not be brother of a, because b may be sister of a. False. Note:- When any one property is not satisfied we say that the relation is not an equivalence relation. Example 11:- Let A = {members of a family}. The relation R means 'is the father of'. S..
: If aRb then bRa. Let a be brother of b then b may not be brother of a, because b may be sister of a. False. Note:- When any one property is not satisfied we say that the relation is not an equivalence relation. Example 11:- Let A = {members of a family}. The relation R means 'is the father of'. S..Summary Relations and Functions
>Relation from a set A to a set B is a subset of A x B. - A relation R on a set A is reflexive if a R a, " a A- A relation R on a set A is symmetric if a R b b R a. - A relation R on a set A transitive if a R b and b R c a R c. A relation R is said to be an equivalence relation on A if it is reflex..
Function Solved Examples
Reasons: (i) (0, 5), (0, 1) pairs make it one - many, one - many is not a function. (ii) Pre-image 2 does not have an image in B. It becomes easy to discuss a function with the help of an arrow diagram. Given A = {-2, -1, 0, 1, 2} and B = {-3, -1, 1, 5}. list the elements of S = {(x, y): ..
Reasons: (i) (0, 5), (0, 1) pairs make it one - many, one - many is not a function. (ii) Pre-image 2 does not have an image in B. It becomes easy to discuss a function with the help of an arrow diagram. Given A = {-2, -1, 0, 1, 2} and B = {-3, -1, 1, 5}. list the elements of S = {(x, y): ..Function Solved Examples Reasons: (i) (0, 5), (0, 1) pairs make it one - many, one - many is not a function. (ii) Pre-image 2 does not have an image in B. It becomes easy to discuss a function with the help of an arrow diagram. Given A = {-2, -1, 0, 1, 2} and B = {-3, -1, 1, 5}. list the elements of S = {(x, y): ..
Reasons: (i) (0, 5), (0, 1) pairs make it one - many, one - many is not a function. (ii) Pre-image 2 does not have an image in B. It becomes easy to discuss a function with the help of an arrow diagram. Given A = {-2, -1, 0, 1, 2} and B = {-3, -1, 1, 5}. list the elements of S = {(x, y): ..The Biconditional statement
If two simple statements p and q are connected by the connective 'if and only if', then the resulting compound statement is called the biconditional statement. Symbolically it is represented by p q. Example: An integer is even if and only if it is divisible by 2. It is a biconditional ..
If two simple statements p and q are connected by the connective 'if and only if', then the resulting compound statement is called the biconditional statement. Symbolically it is represented by p q. Example: An integer is even if and only if it is divisible by 2. It is a biconditional ..See what our Users say :
I love the interaction and ability to explain the process of math problem in depth! Would like see the same for all future lessons one on one! THANK YOU!!!
Even though I don't feel good, the tutor helped me by totally helping me understand!
This Tutor Vista is GREAT! loved this session, it helped me heaps.
The tutors are amazing. They are very committed in helping students solve the questions and explains all the steps beautifully. So 5 stars for Tutor Vista.
Looking for More Help!
