Question

The function ? ? can be determined from the function (1 + ?)? ? by right division (1 + ?)? ? /(1 + ?).

(5 pts) Write a function MyExp.m that takes in any array ? and returns its exponent ? ? by using the function OnePxExp() and the right division by (1 + ?).

Use the function in:

(a) (2 pts) the command window to calculate ? −5 and ? 3 . Use a tolerance of 1E-12 in OnePxExp(). Compare your output of MyExp() and the built-in exp() in format long.

(b)(8 pts) a script file HW07P3. m to make plots of the function ? = sin 2? ? 0.2? and its 1st derivative ? ′ with −3 ≤ ? ≤ 6. Your script must do the following:

i. Close all opened figure window if any

ii. Create the variable −3 ≤ ? ≤ 6 with 100 constant linear spacing elements

iii. Determine ?(?) and ? ′ (?), using the function MyExp() and the built-in sin() functions with elementwise operations,

iv. Use one plot command to plot the 2 line graphs in one plot with the same axes. Use different line style and color for each line (DO NOT USE MARKERS) with a linewidth of 1. Label your axis and add a title, legend and grid lines to your plot,

Answer 1

%since OnePxExp is not provided, i cant show the outcome. If any error occurs, please provide that file

%Function file

function y = MyExp(x)
y=OnePxExp(x,1E-12)./(1+x);

%script

%a
format long
MyExp(-5)
exp(-5)
MyExp(3)
exp(3)

format

%b
close all
t=linspace(-3,6,100);
y=sin(2*t).*MyExp(.2*t);
dy=2*cos(2*x).*MyExp(x/5) + (sin(2*x).*MyExp(x/5))/5;
plot(t,y,':r','LineWidth',1,t,dy,'--g','LineWidth',1)
xlabel('t')
ylabel('y')
title('HW07P3')
legend('y','y''')
grid on