Overview of Sandwich Theorem or Squeeze Theorem

QUICK OVERVIEW

• If two functions squeeze together at a particular point, then any function trapped between them will get squeezed to that same point.
• The Squeeze Theorem deals with limit values, rather than function values.
• The Squeeze Theorem is sometimes called the Sandwich Theorem or the Pinch Theorem

GRAPHICAL REPRESENTATION

Formal Statement:

Suppose f(x)≤g(x)≤h(x)$f(x)\le g(x)\le h(x)$ for all x in an open interval about 
$a$ (except possibly at 
$a$ itself). Further, suppose

limx→af(x)=limx→ah(x)=L${\displaystyle \underset{x\to \mathrm{a }}{lim}f(x)=\underset{x\to \mathrm{a }}{lim}h(x)=L}$

Then, limx→ag(x)=L

Some Mathematics quotes..

Mathematics Quotes

• Pure mathematics is, in its way, the poetry of logical ideas. ...
• I must study politics and war that my sons may have liberty to study mathematics and philosophy. ...
• We will always have STEM with us. ...
• Without mathematics, there's nothing you can do. ...
• Mathematics is the art of giving the same name to different things

Application of linear algebra

Key Words can help us solve mathematical word problems.

Tips for solving problems in mathematics

Trigonometric Important formulas

Some informations regarding Mathematics

01.  The life line of today's time, Google search engine is a term which is derived from word “googol” which is a mathematical term for the number 1 followed by 100 zeros which reflect infinite amount of search on the internet.

02. The debate is going on for a long time now. Americans called mathematics “math” saying that the function of the same is a singular noun and with that logic, they prefer saying “math” which is singular too. But then there are people who call it Maths but we are not covering that part.

03. Did you know that one of the most important numbers, Zero is not represented in the Roman numerals. Derived from Arabic word, ‘sifr’, it is known from a variety of other names like naught, zip, nil and zilch.

04. Confusing as it may sound after the heading, the weirdly interesting thing is that the word “hundred” is derived from another word “hundrath” which actually means 120. Not very logical thing for this logic subject!

05. This debate is going on for a long time now. Americans called mathematics “math” saying that the function of the same is a singular noun and with that logic, they prefer saying “math” which is singular too. But then there are people who call it Maths but we are not covering that part.

Five amazing facts in mathematics

1. (6 × 9) + (6 + 9) = 69

2. The most popular favourite number is 7.

         (Nearly 3000 people, around 10% of the total asked, chose 7 as their favourite number in an online poll by Alex Bellos. The second most popular was 3.)

3. 0 .999999... = 1

         (If 10N = 9.9999...

Then N = .9999....

Subtract N from 10N, leaving you with 9N=9.

So then N=1. But we already know that N=.9999... as well.

So 1=.9999....)

4. 10! seconds is exactly 6 weeks.

         (10! means 10 factorial. 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3628800 seconds. Which is 42 days, or 6 weeks, exactly.)

5.A pizza that has radius "z" and height "a" has volume Pi × z × z × a.

          [Because the area of a circle is Pi multiplied by the radius squared (which can be written out as Pi × z × z). Then you multiply by the height to get the total volume.]

Definition of Row matrix, Column Matrix, Square Matrix, Diagonal Matrix and Symmetric Matrix

Row Matrix: A row matrix is a matrix with only one row. Its order would be 1 X C, where C is the number of columns. For example, here's a row matrix of the order 1 X 5: 

Column Matrix

A column matrix is a matrix with only one column. It is represented by an order of R X 1, where R is the number of rows. Here's a column matrix of the order 3 X 1: 

Square Matrix

A matrix where the number of rows is equal to the number of columns is called a square matrix. Here's a square matrix of the order 2 X 2:

Diagonal Matrix

A diagonal matrix is a square matrix where all the elements are 0 except for those in the diagonal from the top left corner to the bottom right corner. Let's take a look at a diagonal matrix of order 4 X 4: 

Symmetric Matrix

A matrix whose transpose is the same as the original matrix is called a symmetric matrix. Only a square matrix can be a symmetric matrix. The transpose of a matrix is another matrix that is formed by switching the rows and columns of a given matrix. The given matrix A is a 3 X 3 symmetric matrix, since it's the same as its transpose AT. 

Mathematical symbols..

Volume formulae for three dimension figures

Role of Play in Child Development