Answer to Question #7245 in Calculus for Kevin

Question

for each of the following function sketch three level curves in xy-plane labeling each one with its Z-value
(1) f(x,y) = x - 2y
(2) g(x, y) = 3x^2 + 3y^2
(3) h(x,y) = intergral of (2t)dt, from y to x.

Answer 1

For this question, you may use this site: https://www.archimy.com/
(1) Plane
# Grid
xgrid = 1
ygrid = 1

# Calculations
z = x - 2*y

(2) Paraboloid
# Grid
xgrid = 20
ygrid = 20

# Calculations
z = 3*x^2 + 3*y^2
(3) hyperbolic paraboloid: intergral of (2t)dt, from y to x = t^2 | from y to x = x^2 - y^2;

# Grid
xgrid = 20
ygrid = 20

# Calculations
z = x^2 - y^2
or take a look here:
(1) https://www.wolframalpha.com/input/?i=plot+x+-+2*y
(2) https://www.wolframalpha.com/input/?i=plot+3*x%5E2+%2B+3*y%5E2
(3) https://www.wolframalpha.com/input/?i=plot+x%5E2+-+y%5E2