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comet command to determine if you have
the correct set of parametric equations.
Note: I was a bit frustrated that Matlab didn't have a function for this, so I searched the technical notes at the Mathworks and found this technical note:
I then did the following:
t=linspace(0,2*pi,500).'; x1=3*sin(t);y1=2*cos(t);x2=-3+cos(t);y2=1+sin(t); X=[x1,x2];Y=[y1,y2]; comets(X,Y) close all, comets(X,Y)
This allowed me to see that there were two points of intersection, but only one "collision point."
polartrc
to aid in visualizing the area to be sketched in exercises #27 and 29
on page 683. Obtain a printout of each result. Use integration to find
the designated area.
>> format compact >> syms x y z >> u=x^(y/z) u = x^(y/z)Now, the partial derivative with respect to x:
>> ux=diff(u,x)
ux =
x^(y/z)*y/z/x
>> pretty(ux)
(y/z)
x y
--------
z x
Similarly, the derivative with respect to z:
>> uz=diff(u,z)
uz =
-x^(y/z)*y/z^2*log(x)
>> pretty(uz)
(y/z)
x y log(x)
- ---------------
2
z
| (a,b) | f(a,b) | fxx(a,b) | fxx(a,b)fyy(a,b)-f2xy(a,b) | Classification |
|---|---|---|---|---|
| (1,2) | 8 | -4 | (2)(2)-(1)2=3>0 | local maximum |