Question

3. Given the parametric equations x = 3t /1 + t^3 and y = 3t^2 /1 + t^3 . a) Show that the curve produced also satisfies the equation x^3 + y^3 = 3xy. b) Compute the limits of x and y as t approaches −1: i. from the left ii. from the right c) To avoid the issue in part b), graph the curve twice in the same command, once for −5 < t < −1.5 and once for −0.5 < t < 5. d) Repeat part c) using the domains −100 < t < −1.5 and −0.5 < t < 100. In a print command, state how this plot is different from the plot in part c)

Answer 1

%%Matlab code for plotting x and y for various t
clear all
close all

%function for x and y
x=@(t) 3.*t./(1+t.^3);
y=@(t) 3.*t.^2./(1+t.^3);

%all t values
t1=linspace(-5,-1.5);
t2=linspace(-0.5,5);

hold on
plot(x(t1),y(t1))
plot(x(t2),y(t2))

%all t values
t1=linspace(-100,-1.5,1000);
t2=linspace(-0.5,100,1000);

plot(x(t1),y(t1))
plot(x(t2),y(t2))

legend('-5<t<-1.5','-0.5<t<5','-5<t<-1.5','-0.5<t<100','location','best')
xlabel('x')
ylabel('y')
title('x vs. y plot')

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