Chapter 3, Problem 1P

To determine

To calculate:

The value of $y$ in equation $y=x^2-\frac{x}{x+3}$ for the given values of $x$ using element-by-element operations: $0,1,2,3,4,5,6,7$.

Answer to Problem 1P

Solution:

The calculated values of $y$ is $00.753.68.515.428624.37535.666748.3$.

Explanation of Solution

The given values of $x$ is $0,1,2,3,4,5,6,7$.

The stated equation is,

$y=x^2-\frac{x}{x+3}$         .......(1)

Substitute the value $x=0$ in the above equation.

$\begin{array}{c}y=x^2-\frac{x}{x+3}\\ y=0-\frac{0}{0+3}\\ =0\end{array}$

Substitute the value $x=1$ in equation (1).

$\begin{array}{c}y=x^2-\frac{x}{x+3}\\ y=1^2-\frac{1}{1+3}\\ =0.75\end{array}$

Substitute the value $x=2$ in equation (1).

$\begin{array}{c}y=x^2-\frac{x}{x+3}\\ y=2^2-\frac{2}{2+3}\\ =3.6\end{array}$

Substitute the value $x=3$ in equation (1).

$\begin{array}{c}y=x^2-\frac{x}{x+3}\\ y=3^2-\frac{3}{3+3}\\ =8.5\end{array}$

Substitute the value $x=4$ in equation (1).

$\begin{array}{c}y=x^2-\frac{x}{x+3}\\ y=4^2-\frac{4}{4+3}\\ =15.4286\end{array}$

Substitute the value $x=5$ in equation (1).

$\begin{array}{c}y=x^2-\frac{x}{x+3}\\ y=5^2-\frac{5}{5+3}\\ =24.375\end{array}$

Substitute the value $x=6$ in equation (1).

$\begin{array}{c}y=x^2-\frac{x}{x+3}\\ y=6^2-\frac{6}{6+3}\\ =35.6667\end{array}$

Substitute the value $x=7$ in equation (1).

$\begin{array}{c}y=x^2-\frac{x}{x+3}\\ y=7^2-\frac{7}{7+3}\\ =48.3\end{array}$

The calculated values of $y$ is $00.753.68.515.428624.37535.666748.3$.

Write the MATLAB script that calculates the equation $y=x^2-\frac{x}{x+3}$ for the given values of $x$

: $0,1,2,3,4,5,6,7$.

MATLAB Code:

x = [0:7]

% Define the variable x.

y = x.^2-(x)./(x+3)

% Calculate the value of the equation.

Save the MATLAB script with name, chapter3_56830_3_1P.m in the current folder. Execute the script by typing the script name at the command window to get the answer for equation $y=x^2-\frac{x}{x+3}$ for the given values of $x$

: $0,1,2,3,4,5,6,7$.

Result:

Conclusion:

Therefore, the calculated values of $y$ is $00.753.68.515.428624.37535.666748.3$.