...But I'm struggling!
A circle in R^3, ie 3D space is written as: f(x,y)= x^2+ y^2
If we want to draw level curves we give the function different values of C, for example:
C= 1 --> x^2+ y^2 = 1, This will give us a circle with the center in (0,0) and the radius = sqrt(1)=1
BUT what changes when we have x^2+ 4y^2
What does the 4 change, does it change the centre of the circle?
Also, how should one sketch 1< x^2+y^2 (less than or equal to 4) in the XY-plane?
Also 2: The temperature in a point (x,y,z) in a body is described by the function T(x,y,z)=x^2+y^2+z^2+2x-2y (degrees celsius). Describe the areas of the body where the temperature is :
a) larger than 2 degrees celsius
b) smaller than 3 degrees celsius
The last example is like Spanish for me, and I'm not a Spanish speaking person...
An answer to any of the questions is highly appreciated...