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@Malik-Qasim said in MTH643 Assignment 1 Solution and Discussion:

plz written sol today is extend day

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In parametric form the circle of radius 1 centered at (0, 0) can be expressed in parametric form
as x = cos(2 π t) and y = sin(2 π t) where t is from 0 to 1.

https://youtu.be/57BiI_iD3-U

Question # 1
In parametric form the circle of radius 1 centered at (0, 0) can be expressed in parametric form
as x = cos(2 π t) and y = sin(2 π t) where t is from 0 to 1.
Graph the circle with given parametric equations in MATLAB with 1. plot function2. ezplot function

Answer 1:

t= 0:0.01:1;
x = cos(2pit);
y = sin(2pit);
plot(x,y)
And for figure 2:
ezplot(‘x^2+y^2=1’)

Answer 1:
Using plot

Using ezplot:

Question # 2
22222
Draw the contour plot of lemniscate x − y = (x +y ) . You can take any range for the
meshgrid.

Answer 2:

x = linspace(-2pi,2pi);
y = linspace(0,4*pi);
[X,Y] = meshgrid(x,y);
Z = X-Y-(X+Y);
contour(X,Y,Z)

Question # 3
Find the sixth derivative of the following given function using MATLAB
f (x) = sin(4x2 3) +
Answer 3:

syms x
f = sin(4x^2/3);
diff(f,6)
We get:
ans =
(163840x^4cos((4x^2)/3))/81 - (2560cos((4x^2)/3))/9 + (20480x^2sin((4x^2)/3))/9 - (262144x^6sin((4x^2)/3))/729https://www.coursehero.com/qa/attachment/12556913/https://www.coursehero.com/qa/attachment/12557005/https://www.coursehero.com/qa/attachment/12557153/