# Answer to Question #7245 in Calculus for Kevin

Question #7245

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.

(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.

Expert's answer

For this question, you may use this site: http://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) http://www.wolframalpha.com/input/?i=plot+x+-+2*y

(2) http://www.wolframalpha.com/input/?i=plot+3*x%5E2+%2B+3*y%5E2

(3) http://www.wolframalpha.com/input/?i=plot+x%5E2+-+y%5E2

(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) http://www.wolframalpha.com/input/?i=plot+x+-+2*y

(2) http://www.wolframalpha.com/input/?i=plot+3*x%5E2+%2B+3*y%5E2

(3) http://www.wolframalpha.com/input/?i=plot+x%5E2+-+y%5E2

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