Thread: level curves

how do you plot level curves without the use of a computer/calculator e.g. in an exam

f(x,y)=x^2-y^2?

Thanks for any help

Check this out

plot f(x,y)=x^2-y^2 - Wolfram|Alpha

thanks for the reply!, but i was meaning more in an exam without using wolfram/maple.....
I mean how am I supposed to know that is what the level curves of the function look like?
Do you just learn this by becoming familiar with different types of functions?
I am revising for my several varible calculus exam so that is what my questions is in reference to;
Thanks for any help

Originally Posted by hmmmm

thankI mean how am I supposed to know that is what the level curves of the function look like?

Well that's what a lot of people do, although you can begin to shape the function yourself by finding critical points and their nature. You can also test the functions behaviour using limits i.e. its value as it approaches particualr values, i.e. 0 or infinity.