Oh and another question.
According to the notes my teacher gave me,
The equation of a circle is r^2 - x^2 - y^2 = 0 where r is the radius.
While the equation for a circle disk(half space) is
r^2 - x^2 - y^2 >= 0
Why is this so? And why does half space mean in 2D?
How to define a solid cyclinder or any solid objects parametrically?
I can't figure out what do I do with the z axis for example a Cylinder :
x = 0.5*cos(theta)
y = sin(theta)
0*pi <= theta <= 2*pi
This will make an eclipse.
But wad about z?
I know we have to stretch z to the...
Erm... not that, I am trying to define a Sphere using VRML a 3D programming language. My teacher gave us this, its derive from the equation of a Sphere :
parameters [0.0001 6.282 0.0001 3.141]
definition "
x=cos(u)*cos(v);
y=cos(u)*sin(v);
z=sin(u);"
Parameter actually just means u's range is...
I used the formula for a Sphere and I got only half a Sphere :
x=cos(u)*cos(v);
y=sin(u)*cos(v);
z=sin(v);
Basically u = 0.0001 to 6.282 and v = 0.0001 to 3.141, its a piece of programming code but the logic is the same.
Erm..., did I do anything wrong?
Putting it in the layman terms does it mean :
x = r cos(u)
y = r sin(u)
0 <= u <= 2 pi
This is to draw the circle, a ratio of a circle is 2 pi.
x = r cos(u)cos(v)
y = r sin(u)cos(v)
z = r sin(v)
0 <= u <= 2 pi
0 <= v <= pi
The extra stuff is to make the circle "pop up" till...
The equation for a circle is
x = r cos(u)
y = r sin(u)
Where u is 0 <= u <= 2 pi, because 2 pi is for calculating circle.
While a sphere is
x = r cos(u)cos(v)
y = r sin(v)cos(v)
z = r sin(v)
Where u is the same, 2 pi but v is 0<= v <= 1 pi.
Why only 1 pi for v? and not 2...
Its 2^{n/2}
And oops my bad, I meant how do I differentiate lg^2 x n where lg is log base 2.
Since lg is log base 2 and its to the power of 2 wouldn't it be be 1? and if we differentiate n its 1?
How do you differentiate :
2^n/2?
You can't you just use the power rule?
The correct answer is 2^n/2 (In^2) 1/2
lg^2 x n
Where lg is log base 2.
The correct answer is 2lgn 1/n^2 . 1/n
Why is this so? Isn't lg^2 = 1? And differentiate n and we get 1?
Sorry if I sound...
About Big-Oh/Big Omega/Big Theta :
Limit of n approching inifinity f(n)/g(n) = c < inifinity means its Big-Oh
Limit of n approching inifinity f(n)/g(n) = c > 0 means its Big-Omega
Limit of n approching inifinity f(n)/g(n) = 0 < c < inifinity means its Theta
Does that mean that they are...
Ah I see. Therefore, is it safe to say for simple functions like (4n + 3)/n I can just sub in a few number to determine where the limit is leaning towards and therefore get the limit.
But for really large number like n/(e to the power of n), where its hard or I can't sub in any numbers and...
Oops my bad, my bad. What I meant was (4n + 3)/n, not 4n + 3/n.
Is both f(n) and g(n) reaching infinity now? But no L Hospital was used in the example though.