Troubleshooting Level Curves: Tips for Sketching and Graphing

[ezdn]

im having trouble with sketching a level curve

ex. equation: f(x,y) = x^2 + 2y^2

i can't run it .. (edit: sorry, -cant run it by matlab) .. :(

cant solve can't graph can't all ... in short, can't any attempt at a solution :(((
thank for your help ..

 

[Mark44]

1. I am having trouble with sketching a level curve



2. ex. equation: f(x,y) = x^2 + 2y^2

i can't run it :(



3. can't any attempt at a solution :(((

What do you mean you can't "run it?"

Level curves are two-dimensional slices of a surface in three dimensions. Pick several values for z and sketch graphs of the resulting curves.

For example, if z = 0, what's the graph of the equation x^2 + 2y^2 = 0 look like?
If z = 1, what's the graph of the equation x^2 + 2y^2 = 1 look like?
If z = -1, what's the graph of the equation x^2 + 2y^2 = -1 look like?

And so on...

 

[Blitzy89]

im having trouble with sketching a level curve

ex. equation: f(x,y) = x^2 + 2y^2

i can't run it :( can't solve can't graph can't all ... in short, can't any attempt at a solution :(((






thank for your help ..

When I had to sketch level curves, my teacher showed me a nice and easy to understand method:
Your equation is f(x,y) = x^2 + 2y^2 . Write it as z = x^2+2y^2
which could also be re-written as z=(x^2/1)+(y^2/1/2)

Now that you have a clearer idea of what this could represent : if z=k a constant then for a certain z you have an ellipse of k=(x^2/1)+(y^2/1/2)
Sketch it for some values and then connect the elements together. Since z can't be negative (x and y are both squared) it will be something like a parabola going up in the z-dir. So I guess it is a paraboloid, where each "slice" taken in z=k plane is an ellipse given by k=(x^2/1)+(y^2/1/2).

 

[ezdn]

thank you for your attention :)