2.2 Completing the basics  (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.