Use of Calculus in Real Life

In this article we are going to discuss about the use of calculus in real life problems step by step concept. The process of contraction the calculus comparable to over screening the real life problems concept and problem in calculus are referred as review use of calculus in real life. This article helps to improve the knowledge the real life for calculus and below the problems are using toll for the help with test calculus. Put down behind the useful get review real life use of calculus to this article. Use of calculus in real life solutions also show below.

Level One Example Real Life Calculus Use Problems:-

Real life calculus use problem 1:-

Integrate the following equation

`int 5x^4+4x^5+5x^3 dx`

Solution:-

Step 1:-

`int 5x^4+4x^5+3x^3 dx`

Step 2:-

`= int5x^4dx + int4x^5dx + int 3 x^3 dx`

Integrating the above equation

We get

Step 3:-

`= (5x^5)/(5) + (4x^6)/ (6) + (3x^4)/ (4)`

Step 4:-

`= (5x^5)/(5) + (4x^6)/(6) +(3x^4)/ (4)`

Step 5:-

`= x^5+ (2x^6)/ (3) + (3x^4)/ (4)`


Real life calculus use problem 2:-

Solve by differentiating the following equation and get the first derivative second derivative and third derivative

`y = 12x^3 + 8x^2+ 4x^5 + x`

Solution:-

Given equation is `y = 12x^3+ 8x^2 + 4x^5 + x`

Step 1:-

To get the 1st derivative differentiate the above given equation

`(dy)/(dx) = 36x^2+16x+20x^4`

Step 2:-

To get the 2nd derivative differentiate the ist derivative

`(d^2y)/ (dx^2) = 72x+16+80x^3.`


Level Two Example Real Life Calculus Use Problems:-

Real life calculus use problem 1:-

Integrate the following equation

`int 8x^4+4x^5+2x^3 dx`

Solution:-

`int 8x^4+4x^5+2x^3 dx`

Step 1:-

`= int 8x^4 dx + int 4x^5 dx + int 2 x^3 dx`

Integrating the above equation

We get

Step 2:-

`= (8x^5)/ (5) + (4x^6)/ (6) + (2x^4)/ (4)`

Step 3:-

`= (8x^5)/(5) + (2x^6)/(3)+ (x^4)/(2)`

Real life calculus use problem 2:-

Differentiate the following equation and get the 1st, 2nd and 3rd derived

`y = 8x^3+4x^2+2x^1+ 12`

Solution:-

Step 1:-

By differentiate the given equation with respect to x to get the 1st derivative

`y= dy/dx =24x^2+8x^1+2.`

Step 2:-

To get the 2nd derived differentiate the 1st derivative of the given equation.

`y = (d^2x)/ (dy^2) = 48x + 8`

Step 3:-

To get the 3rd derived differentiate the 2nd derivative of the given equation.

`y= (d^3x)/ (dy^3) = 48.`

Function of X Graph

In the mathematics concept, a polynomial function is an expression of finite measurement, lengthwise it is constructed from variables and constant values, using only the operations of addition, subtraction, multiplication, and non-negative, whole-number exponent values. For example, 3x2 − 5x + 9 is a polynomial, but 3/x2 − 5/x + 9x3/2 is not, because its second term involves division by the variable x and because its third term contains an exponent that is not a whole number. In this article we shall discuss about function of x graph.

Sample Problem for Function of X Graph:

Problem 1:

Solve the function f(x) = 2 x + 3.find the coordinate of vertex of the triangle formed by lines and the x axis in graphing polynomial.

Solution:

Given:

        F(x) = 2x + 3

We take f(x) = -y

We get,   2 x – y + 3 = 0

        Thus, 2x – y = -3

                        2x = y – 3

Equation (1) is divided by -1. We get

                              -2x = -y + 3

                              y = 2x + 3 -------------- (1)


From equation (1) we get the following values

            X         -2         -1           0        1

            Y          -1          1          3         5

Problem 2:

Solve the function f(x) = -x + 4.find the coordinate of vertex of the triangle formed by lines and the x axis in graphing polynomial.

Solution:

Given:

        F(x) = -x + 4

We take f(x) = y

We get,   -x + y + 4 = 0

        Thus, -x + y = -4

                        -x = -y – 4

                         y = x - 4

From equation (1) we get the following values

            X      0            1           2           3

            Y     -4           -3          -2           -1

Function of X Graph:problem 3:

Solve the function f(x) = -2 x - 3.find the coordinate of vertex of the triangle formed by lines and the x axis in graphing polynomial.

Solution:

Given:

        F(x) = -2x - 3

We take f(x) = -y

We get,   -2 x - y - 3 = 0

        Thus, -2x - y = 3

                          -2x = y + 3

Equation (1) is divided by -1. We get

                              2x = -y -3

                              y = -2x - 3 -------------- (1)

From equation (1) we get the following values

            X         -2         -1       0            1          

            Y          1         -1      -3           -5

     

Quadrilateral Right Angle

Quadrilateral is a two dimensional figure which has four sides and four inside angles. In Quadrilateral, All sides are equal lengths and equal angles. It is also called as four sided polygon with four angles. Quadrilateral is a type of plane geometry. There are many quadrilaterals in geometry. They are square, rectangle, rhombus, and parallelogram, and kite, trapezoid. Let us learn about the right angle quadrilaterals.



Quadrilateral Right Angle:



An internal angle that is equal to 90° is said to be right angle.



These are various kinds of right angles.

Various properties of Quadrilateral:

• All quadrilaterals contain 4 surfaces.
• A square has acquired 4 surfaces of identical length and 4 right angles.
• A Rhombus has acquired 4 sides of identical length and opposite sides is parallel and angles are identical.
• The rectangle holds 4 right angles. It has acquired 2 pairs of identical length surface.
• A trapezium has acquired one pair of parallel sides.
• A kite has acquired two pairs of surface next to each other that have identical length.

Types of Quadrilaterals with Right Angles:

Square:



A square has equivalent surface and each angle is a right angle. As well as, opposite surface are parallel.

Rectangle:



Rectangle is a shape with 4 sides where each angle is a right angle. As well as, differing surface are parallel and of identical length.

Rhombus:



A rhombus is figure with 4 sides where all surface have identical length. Rhombus does not have the right angle. But the diagonal got right angles. Also differing surface are parallel and opposite angles are identical.

Kite:



It has two pair of surface. Every pair is prepared up of adjacent sides that are identical in length. The angles are equivalent where the pairs get together. Diagonals get together at a right angle, and one of the diagonal bisects another.

Trapezium:



Both of these are kind of trapezium. Every of them have dissimilar properties in the quantity of right angles. But each have 4 surface and one pair of parallel surface.

Set Multiple Values

The definition of set is group of object. Collection of whole number, collection of natural numbers, and collection of fraction numbers it is called the some examples of set multiple values. The set symbol is represented the { }. The example of set multiple value is {4, 5, 7, 6}. Next we discuss about this articles set multiple values.

First Problem of Set Multiple Values

Problem 1: set multiple values

If A = {5, 3, 6, 2, 7, 13 ,15} and B  = {5, 3, 6, 2, 7}  find out n(A), n(B), n(A `uu` B)and n(A `nn` B) and to prove n (A `uu`B) = n (A) + n (B) – n (A `nn`B)

Solution:

A = {5, 3, 6, 2, 7, 13, 15}

B = {5, 3, 6, 2, 7}

A `uu` B = {5, 3, 6, 2, 7, 13, 15}

A `nn` B = {5, 3, 6, 2, 7}

n (A) = 7

n (B) = {5},

n (A`uu` B) = {7},

n (A`nn` B} = {5}

n (A) + n (B) – n (A `nn` B)

7 + 5 - 5

= 7

The A `uu` B = 7

So,

n (A`uu` B) = n (A) + n (B) – n (A `nn` B)

Second Problem of Set Multiple Values

Problem 2: set multiple values

If X = {7, 9, 4, 2, 5} and Y = {7, 9, 4, 2, 5, 13, 14} find n(X), n(Y) n(X `uu` Y), n(X `nn` Y) and to verify the identity n (X uu Y) = n (X) + n (Y) – n (X `nn` Y)

Solution:

X = {7, 9, 4, 2, 5}

Y = {7, 9, 4, 2, 5, 13, 14}

{X `uu` Y} = {7, 9, 4, 2, 5, 13, 14}

{X `nn` Y} = {7, 9, 4, 2, 5}

n (X) = {5}

n (Y) = {7}

n(X `uu` Y) = {7}

n(X `nn` Y) = {5}

n (X) + n (Y) – n (X `nn` Y)

= 5 + 7- 5

= 12 - 5

= 7

Here X `uu` Y = 7

So,

n (X`uu` Y) = n (X) + n (Y) – n (X `nn` Y)

Place Value Tenths Hundredths

Place value can describe the value of all numbers .The place value can be used to point out the position of a mathematical system. It is tremendously helps you to read the numerals by its places. Place value is the value which is given to the digit by popular quality .In this article we shall discuss the place value of tenths hundredths.

Place Value Tenths Hundredths:

The place values from one to ten thousand and to ten thousandth are as follows.

For example for the value 11111.11111

1 – Place value one.

10 = place value Ten.

100 – Place value Hundred.

1000 – Place value thousand.

10000 – Place value ten thousand.

1÷10 =0.1- place value tenth.

1÷100= 0.01- place value hundredth.

1÷1000=0.001- place value thousandth.

1÷10000=0.0001- place value ten thousandth.

1÷100000=0.00001- place value hundred thousandth.

Examples Problems on Place Value:

Ex:1 Round the following number to the hundredth place value 746.839256

Sol:

Given that the number 746.839256

From the given number on the left side from the decimal point,

7 indicates Place value Hundred.

4 indicate place value ten.

6 indicate Place value one.

From the given number on the right side from the decimal point,

8 indicate tenth place value.

3 indicate hundredth place value.

9 indicate thousandth place value.

2 indicate ten thousandth place value and so on.

As the question is to encircle the number 746.839256 to the hundredth place value.

The answer is 746.83

Ex:2 Add the numbers 1563.457 and 1999.336 and round the solution to the hundredth place value.

Sol:

Adding the numbers we get




The solution is  3562.793

From the given number on the left side from the decimal point,

3 indicate place value thousand.

5 indicate Place value Hundred.

6 indicate place value ten.

2 indicate Place value one.

From the given number on the right side from the decimal point,

7 indicate tenth place value.

9 indicate hundredth place value.

3 indicate thousandth place value.

As the question is to encircle the number 3562.793 to the tenth place value.

The answer is 3562.8 because the place value nearest to hundredth (7) is greater than 5(9).


Ex:3 Round the following number to the tenth place value 876.473957

Sol:

Given that the number 876.473957

From the given number on the left side from the decimal point,

8 indicates Place value Hundred.

7 indicate place value ten.

6 indicate Place value one.

From the given number on the right side from the decimal point,

4 indicate tenth place value.

7 indicate hundredth place value.

3 indicate thousandth place value.

9 indicate ten thousandth place value and so on.

As the question is to encircle the number 876.473957to the tenth place value.

The answer is 876.5

Ex:4 Add 388.8018 and 100.1111 and round the solution to tenth place value.

Sol:

Adding 388.8018 and 100.1111 we get,



The solution is  488.9129

From the given number on the left side from the decimal point,

4 indicate Place value Hundred.

8 indicate place value ten.

8 indicate Place value one.

From the given number on the right side from the decimal point,

9 indicate tenth place value.

1 indicate hundredth place value.

2 indicate thousandth place value.

9 indicate ten thousandth place value.

As the question is to encircle the number 488.9129 to the tenth place value.

The answer is 488.9

Practice Problems on Place Value:

Q:1 Round the following number to the hundredth place value 44776.76234

Ans:

The answer is 44776.76

Q:2 Round the following number to the tenth place value 56256353.3564847

Ans:

The answer is 56256353.4

Place Value Number System

The Place Value of a digit in a number system is the digit multiplied by 100, 101, 102, 103, 104, 105, 106, 107, 108, 109,... etc. according as the digit appears in the number system as once, tens, hundreds, thousands, ten thousand, hundred thousand, million, billion, trillion respectively.  Example for place value number system: 3333333333333. This can be represented as three trillion three hundred and thirty three billion three hundred and thirty three million three hundred and thirty three thousand and three hundred and thirty three. Here we are going to see in detail about place value number system.

Ones:

Ones is the word which means the number 1. The place value of ones is one. This is the right most number, For any number the right most number or the first number in the right side will be ones

Example problem:

1)  Find the ones place value in the number 85,494

Solution:

The ones place value in the number 85,494 is 4

2)  Find the ones place value in the number 856,490

Solution:

The ones place value in the number 856,490 is 0

Tens:

Tens is the word which means teh number 10. The place value of tens is two.

Example problem:
1)  Find the tens place value in the number 325,968

Solution:

The tens place value in the number 325,968 is 6

2)  Find the tens place value in the number 16,824

Solution:

The tens place value in the number 16,824 is 0

Hundreds:

Hundred is the word which mean the number 100, the word hundred is also known as centum. The place value of hundreds is three.

Example problem:

1)  Find the hundreds place value in the number 78,256

Solution:

The hundreds place value in the number 78,256 is 2

2)  Find the hundred place value in the number 954,263

Solution:

The hundred place value in the number 954,263 is 2

Thousands:

Thousand is the word which means the number 1,000. The place value of thousand is four. Ten thousand and hundred thousand comes under the category of thousand.

Example problem:

1) Find the thousands place value of the number 479,258

Solution:

The thousands place value of the number 479,258 is 9

2) Find the ten thousands place value of the number 479,258

Solution:

The ten thousands place value of the number 479,258 is 7

3) Find the hundred thousand place value of the number 479,258

Solution:

The hundred thousands place value of the number 479,258 is 4

Millions:

Million is the word which means the number 1,000,000. The place value of million is seven. Ten million and hundred million comes under the category of million.

Example problem:

1)    Find the million place value of 951,654,259

Solution:

The million place value of the number 951,654,259 is 1

2)    Find the ten million place value of 951,654,259

Solution:

The ten million place value of the number 951,654,259 is 5

3)    Find the hundred million place value of 951,654,259

Solution:

The hundred million place value of the number 951,654,259 is 9

Billions:

Billion is the word which means the number 1,000,000,000. The place value of billion is ten. Ten billion and hundred billion comes under the category of billion.

Example problem:

1)    Find the Billion place value of 907,789,246,846

Solution:

The Billion place value of the number 907,789,246,846 is 7

2)    Find the ten Billion place value of 907,789,246,846

Solution:

The ten Billion place value of the number 907,789,246,846 is 0

3)    Find the hundred Billion place value of 907,789,246,846

Solution:

The hundred Billion place value of the number 907,789,246,846 is 9

Trillions

Trillion is the word which means the number 1,000,000,000,000. The place value of trillion is thirteen. Ten Trillion and hundred Trillion comes under the category of Trillion.

Example problem:

1) Find the Trillion place value of 456,758,246,349,246

Solution:

The Trillion place value of the number 456,758,246,349,246 is 6

2)    Find the ten Trillion place value of 456,758,246,349,246

Solution:

The ten Trillion place value of the number 456,758,246,349,246 is 5

3)    Find the hundred Trillion place value of 456,758,246,349,246

Solution:
The hundred Trillion place value of the number 456,758,246,349,246 is 4

Statistics on College Students

Statistics should be help with formal science. These are generating well-organized help of algebraic data among the groups of individuals. In statistics, we are learning help on median, mode, mean and range. Measuring of these problems is extremely easy. For this we are using formulas. Now we will see statistics example problems on the college students.

Statistics Examples for College Students

Example 1:

Find the mean, median for the sequence of numbers, 560,247,281,396,185,160,288.

Solution:

The given numbers are 560,247,281,396,185,160,288.

Mean

Mean is the average of the given number. Calculate the total value of the given sequence.

Sum of the given numbers are = 560+247+281+396+185+160+288

= 2117

Total values are divided by 7 (7 is the total numbers) = `(2117)/(7)`

= 302.43

Median

Middle element of the sorting order of given series is a median.

The sorting order series is 160,185,247,281,288,396,560.

The middle element of the sorting sequence is 281.

So the median is 281.

Example 2:

Find the mode value for the following sequence of numbers, 291,358,640,291,305,291.

Solution:

Given series is, 291,358,640,291,305,291.

Mode is the most repeatedly occurring value of the series.

Here, the number ‘291’ should be occurring three times.

So, the mode value is 291.

Example 3:

Find the range value for the following sequence of numbers, 488,150,362,205,117,250.

Solution:

Given series is, 488,150,362,205,117,250.

Subtract the smallest value from the biggest value of the series is said to be range.

Range = 488 - 117

= 371

Standard Deviation Example for College Students

Let see the learning example for standard deviation in statistics on college students.

Example 4:

Find the standard deviation of the following numbers, 30,59,65,27,16,12,33,22.

Solution:

The given numbers are 30,59,65,27,16,12,33,22.

Establish the mean for the given data.

Mean = `(30+59+65+27+16+12+33+22)/(8)`

= `(264)/(8)`

= 33

Construct the table for finding standard deviation.

x	x-33	(x-33)2
30	-3	9
59	26	676
65	32	1024
27	-6	36
16	-17	289
12	-21	441
33	0	0
22	-11	121
Total		2596

Find (x-m)2 / (n-1) = `(2596)/(8-1)`

= `(2596)/(7)`

= 370.86

Formula of the standard deviation = `sqrt((sum_(i=1)^n (x-m)^2) / (n-1))`

= `sqrt(370.86)`

= 19.26

Thus the standard deviation is 19.26.

These are the few statistics example problems that help on college students.

That’s all about the statistics on college students.