Chapter 7, Problem 1P

To determine

(a)

A user-defined MATLAB function for the given math function $y\left(x\right)=\left(-0.2x^3+7x^2\right)e^{-0.3x}$; the value of $y\left(-1.5\right)$ and $y\left(5\right)$ using this function. (Write the function such that $x$ can be a vector.)

Answer to Problem 1P

Solution:

The value of $y\left(-1.5\right)$ is $\text{25}\text{.7595}$ and $y\left(5\right)$ is $\text{33}\text{.4695}$.

Explanation of Solution

The given function is,

$y\left(x\right)=\left(-0.2x^3+7x^2\right)e^{-0.3x}$

Solve the above equation for $y\left(-1.5\right)$.

$\begin{array}{c}y\left(x\right)=\left(-0.2x^3+7x^2\right)e^{-0.3x}\\ y\left(-1.5\right)=\left(-0.2{\left(-1.5\right)}^3+7{\left(-1.5\right)}^2\right)e^{-0.3\left(-1.5\right)}\\ =\text{25}\text{.7595}\end{array}$

Solve the above equation for $y\left(5\right)$.

$\begin{array}{c}y\left(x\right)=\left(-0.2x^3+7x^2\right)e^{-0.3x}\\ y\left(5\right)=\left(-0.2{\left(5\right)}^3+7{\left(5\right)}^2\right)e^{-0.3\left(5\right)}\\ =\text{33}\text{.4695}\end{array}$

Write the MATLAB code to determine the user-defined MATLAB function for the given math function $y\left(x\right)=\left(-0.2x^3+7x^2\right)e^{-0.3x}$ and calculate the value of $y\left(-1.5\right)$ and $y\left(5\right)$ using this function.

MATLAB Code:

Function file

function y = Chapter7_29864_7_1P(x)

y = (-0.2*x.^3+7*x.^2).*exp(-0.3*x);

Script file

%...............................Script file.....................

x = [-1.5 5];

y = Chapter7_29864_7_1P(x);

disp('The test values for y(x) are:')

disp(y)

Save the MATLAB script with name, Chapter7_29864_7_1P.m in the current folder. Execute the script by typing the script name at the command window to get the code that determines the user-defined MATLAB function for the given math function $y\left(x\right)=\left(-0.2x^3+7x^2\right)e^{-0.3x}$ and calculate the value of $y\left(-1.5\right)$ and $y\left(5\right)$ using this function.

Result:

Conclusion:

Therefore, the value of $y\left(-1.5\right)$ is $\text{25}\text{.7595}$ and $y\left(5\right)$ is $\text{33}\text{.4695}$.

To determine

(b)

To make:

A plot of the given function $y\left(x\right)$ for $-2\le x\le 6$.

Answer to Problem 1P

Solution:

The program is stated as follows.

Explanation of Solution

The given function is,

$y\left(x\right)=0.6x^3{e}^{-0.47x}+1.5x^2{e}^{-0.6x}$

Write the MATLAB code to make the plot of the given function $y\left(x\right)$ for $-2\le x\le 6$.

MATLAB Code:

Function file

function y = Chapter7_29864_7_1P(x)

y = (-0.2*x.^3+7*x.^2).*exp(-0.3*x);

Script file

x = -2:0.1:6;

plot(x,Chapter7_29864_7_1P(x));

title('y(x) = (-0.2x^3 + 7x^2)e^{-0.3x}')

xlabel('x')

ylabel('y')

Save the MATLAB script with name, Chapter7_29864_7_1P.m in the current folder. Execute the script by typing the script name at the command window to get the code to make a plot of the given function $y\left(x\right)$ for $-2\le x\le 6$.

Result:

Conclusion:

Therefore, the program is stated above.