How math deals with Pythagoras theorem and Limit of function

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Pythagoras Theorem

Mathematics is an abstract subject with unique signs, colorful graphs, and diverse shapes and structures in geometry. This amazingly exciting subject sometimes gives tough times, but the addition of some adventure makes it more interesting.

One of the many interesting and adventurous topics there is Algebra, which itself is a diverse topic. Pythagoras Theorem is one of the standard algebraic problems. This theorem is acting as the basics of mathematics, contributing to solving several math issues, particularly Algebra and geometry for centuries now.

In geometry, the triangle with a right angle (90 degrees) gives a long straight line, known as Hypotenuse. In the triangle, this hypotenuse is collectively the area of both base and perpendicular. 

The square of the hypotenuse at the right angle is the sum of the two other sides (base and perpendicular) of the triangle.

A triangle is a collection of three tangents of different angles and lengths attached to each other following the Head to Tail rule. According to this Head to Tail rule, the tangents are attached to each other in a way that one’s tail is attached to another’s head and its head to the other tail forming a triangle.

The triangle with a right angle is used in the Pythagoras Theorem.

As an example calculate the length of the tangents of a right angle triangle

Base= a =4cm

Perpendicular= b =3cm

Hypotenuse = c =5cm

Now take the squares of each value

ax2=16

bx2=9

cx2=25

According to the Pythagoras Theorem, the square of hypotenuse ‘c’ is the sum of both the square values of ‘a’ and ‘b’.

Formula used in Pythagorean theorem

ax2+ bx2 = cx2 

 4×2 + 3×2 = 5×2

=16 + 9 = 25

Pythagorean theorem solver helps to find the steepness of slopes. The slope can be of a hill and mountain. To observe the angles of these slopes, you can use a telescope to look toward the measuring object maintaining a fair distance so that the observations must be clear.  So you can achieve the right angle of the slope.

Why is the Pythagorean theorem important in mathematics?

It is of many uses, and the standard one is to observe the slope and triangles. To observe the types of triangle, acute triangle, obtuse triangle, or the right triangle, you can use the Pythagoras theorem. If the theorem works, it is a right triangle with a square of hypotenuse equal to the sum of both values. If the square hypotenuse is large, it is an obtuse triangle, and if the square of the hypotenuse is small, it is an acute triangle.

This theorem helps in the building of rectangles, obtaining the missing lengths of the triangle.

Applications of Pythagorean Theorem

The real-life applications of limits in our daily life are given as follow:

  • Pythagorean Theorem is used to find the diagonal length of the roof’s slope.
  • It is used in physical construction works like woodworking or architecture etc.
  • Computer and Information technology engineers, Engineering and science engineers, and also construction engineers used this old age formula in their practical work.
  • Pythagorean theorem is also used in two-dimensional navigation.
  • It is also used to find the slope or steepness of high hills or mountains.
  • You can also find the real height of a broken tree by using that Pythagorean theorem.

Related: These are the technology tools which are helpful in educational purpose, you ma also concern may other educational tools and get understandable study of it.

Introduction to Limits

Limit is one of the easiest concepts of calculus. No doubt, If it is easy to understand what are limits, it does not mean that limits can be explained in a single piece of paper. Limit is a vast field of calculus or you may be called the major concept of calculus. 

In limits, there is a continuous change that occurs or we approach toward something so that the minor difference between them can be neglectable.

What is the Limit of a Function?

As we say, every action has a reaction. The same goes here; the function (f) allows every input (x) to have an output (f(x)) function, and yes, it also assigns itself a limit (l), where the function has to stop the input (p). In this case, the output(fx) comes closer to the limit(l), and the initial input(x) comes closer to the final input(p).

Formula

x→alim​f(x)=L

 

The precise definition of Limits

The precise definition of limit is somehow different than its theoretical definition. Also, the definition of limit can help us to learn how limits are important and useable in mathematics or especially in calculus. As it is the base of both derivatives and integration.

The precise definition of limits are given as :

The Limit as some number like “x” approaches to some defined number “c”  should be some outputted number which we will call “L”.

It means that if we approach any function like f(x) to the number “c” but it will not be exactly that “c”, then the whole function f(x) will be equal to L.

Limit of a function mathematics

The limit of a function is the calculation of functions within a limit. It belongs to calculus, and as calculus is a kind of infinite calculation, the limit of a function acts as a pillar to this unstable calculus. Calculus is a scene of inaccuracy and infinity. In other terms, it never determines an accurate answer, calculation, or any solution. There is always the chance of proximity in calculus. The limit of a function is an approx calculation but in less sense. You know the limits of your calculations, and it also gives a range of input till the final output, so you have the privilege to be approximately correct. 

For example, you know the limit of a function is 1, so you also know its inputs, i.e., 0.0,……..0.999 this is the input of function while 1 is the limit of the function.

Applications of Limits

The real-life applications of limits in our daily life are given as follow:

  • Limits are helpful while measuring the magnetic field or electric field etc.
  • It is used to filter out useable information from raw data.
  • Limits are used as real-life approximations of derivatives.
  • Limits are used in the speedometers of our cars.

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