Chapter 3, Problem 1P

To determine

To calculate:

The value of $y$ in equation $y=x^2-e^{0·5x}+x$ for the following values of $x$ using element-by-element operations: $-3,-2,-1,0,1,2,3$.

Answer to Problem 1P

Solution:

The calculated values of $y$ is $5.77691.6321-0.6065-1.00000.35133.28177.5183$.

Explanation of Solution

The given values of $x$ is $-3,-2,-1,0,1,2,3$.

The stated equation is,

$y=x^2-e^{0·5x}+x$ ……(1)

Substitute the value $x=-3$ in the above equation.

$\begin{array}{c}y=x^2-e^{0·5x}+x\\ y={\left(-3\right)}^2-e^{0·5\left(-3\right)}+\left(-3\right)\\ =5.7769\end{array}$

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

$\begin{array}{c}y=x^2-e^{0·5x}+x\\ y={\left(-2\right)}^2-e^{0·5\left(-2\right)}+\left(-2\right)\\ =1.6321\end{array}$

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

$\begin{array}{c}y=x^2-e^{0·5x}+x\\ y={\left(-1\right)}^2-e^{0·5\left(-1\right)}+\left(-1\right)\\ =-0.6065\end{array}$

Substitute the value $x=0$ in equation (1).

$\begin{array}{c}y=x^2-e^{0·5x}+x\\ y={\left(0\right)}^2-e^{0·5\left(0\right)}+\left(0\right)\\ =-1.0000\end{array}$

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

$\begin{array}{c}y=x^2-e^{0·5x}+x\\ y={\left(1\right)}^2-e^{0·5\left(1\right)}+\left(1\right)\\ =0.3513\end{array}$

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

$\begin{array}{c}y=x^2-e^{0·5x}+x\\ y={\left(2\right)}^2-e^{0·5\left(2\right)}+\left(2\right)\\ =3.2817\end{array}$

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

$\begin{array}{c}y=x^2-e^{0·5x}+x\\ y={\left(3\right)}^2-e^{0·5\left(3\right)}+\left(3\right)\\ =7.5183\end{array}$

The calculated values of $y$ is $5.77691.6321-0.6065-1.00000.35133.28177.5183$.

Write the MATLAB script that calculates the value of $y$ in equation $y=x^2-e^{0·5x}+x$ for the following values of $x$ using element-by-element operations: $-3,-2,-1,0,1,2,3$.

MATLAB Code:

x = -3:3;

% Define the variable x.

y = x.^2-exp(0.5*x)+x

% Calculate the value of the equation.

Save the MATLAB script with the name, chapter3_29864_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 $y=x^2-e^{0·5x}+x$ for the given values of $x$ : $-3,-2,-1,0,1,2,3$.

Result:

Conclusion:

Therefore, the calculated values of $y$ is $5.77691.6321-0.6065-1.00000.35133.28177.5183$.