# Level Curves

• Feb 5th 2010, 07:59 AM
eri123
Level Curves
Function: $z=f(x,y)=5-x^2-y^2$
How would you draw a contour plot and label the level curves for z=0, z=1, z=2, z=3, z=4, z=5? Also, how do you find out what the largest and smallest z-values are? Would the smallest be z=0 and the largest be z=5?
• Feb 5th 2010, 08:06 AM
Calculus26
for the level curves z = c = 5- x^2 -y^2

x^2 + y^2 = 5 - c are concentric circles of radius sqrt(5-c)

for c= 0 ,1,2,3,4,5
• Feb 5th 2010, 08:14 AM
dedust
Quote:

Originally Posted by eri123
Function: $z=f(x,y)=5-x^2-y^2$
How would you draw a contour plot and label the level curves for z=0, z=1, z=2, z=3, z=4, z=5? Also, how do you find out what the largest and smallest z-values are? Would the smallest be z=0 and the largest be z=5?

because $x^2 + y^2 \geq 0$ for all $x,y$, then the largest value of $z = 5 - (x^2 + y^2)$ is 5 and the smallest is $- \infty$