# 2.2 Completing the basics  (Page 5/6)

 Page 5 / 6

`cout<<"The circumference of the circle is "`

`<<circumference<<endl;`

`return 0;`

`}`

The output of the above program:

The circumference of the circle is 12.5664

## Focus on problem solving

In this section, we present a programming problem to further illustrate both the use of cin statements to accept user input data and the use of library functions for performing calculations.

Problem: Approximating the Exponential Function

The exponential function e^x, where e is known as Euler’s number (and has the value 2.718281828459045…) appears many times in descriptions of natural phenomena. The value of e^x can be approximated using the following series:

1 + x/1 + x^2/2 + x^3/6 + x^4/24 + x^5/120 + x^6/720 + …

Using this polynomial as a base, assume you are given the following assignment: Write a program that approximates e raised to a user input value of x using the first four terms of this series. For each approximation, display the value calculated by C++’s exponential function, exp(), the approximate value, and the absolute difference between the two. Make sure to verify your program using a hand calculation. Once the verification is complete, use the program to approximate e^4.

Using the top-down development procedure, we perform the following steps.

## Step 1: analyze the problem

The statement of the problem specifies that four approximations are to be made using one, two, three, and four terms of the approximating polynomial, respectively. For each approximation, three output values are required: the value of produced by the exponential function, the approximate value, and the absolute difference between the two values. The structure of the required output display is as below (in symbolic form).

Realizing the each line in the display can only be produced by executing a cout statement, it should be clear that four such statements must be executed. Additionally, since each output line contains three computed values, each cout statement will have three items in its expression list.

The only input to the program consists of the value of x. This will, of course, require a single prompt and a cin statement to input the necessary value.

## Step 2: develop a solution

Before any output items can be calculated, the program needs to prompt the user for a value of x and then accept the entered value. The output display consists of two title lines followed by four lines of calculated data. The title lines can be produced using two cout statements. Now let’s see how the data being displayed are produced.

The first item on the first data output line illustrated in Table 3.4 can be obtained using the exp() function. The second item on this line, the approximation to ex , can be obtained by using the first term in the polynomial that was given in the program specification. Finally, the third item on the line can be calculated by using the abs() function on the difference between the first two lines. When all of these items are calculated, a single cout statement can be used to display the three results on the same line.

how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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