Thread: Level Curves

f(x,y)=(x^2-4x)cos(πy), I need to sketch the level curves for c=0, 1, and -1 of this function for |x|, |y|≤4.

So far I sketched the curves for f=0, and then I do not know how to proceed.

does that say cos(ny)?

Originally Posted by bly2425

f(x,y)=(x^2-4x)cos(πy), I need to sketch the level curves for c=0, 1, and -1 of this function for |x|, |y|≤4.

So far I sketched the curves for f=0, and then I do not know how to proceed.

Ok so I guess the best way to proceed is to remember that a level curve indicates the function at different heights and the c constant is simply a fixed value of z. So immagine looking down on the function at each z value. To sketch the level curve of c = 1 for example, simply subsitute
1 = (x^2-4x)cos(ny) and graph that function, the same for c = -1 etc. so in the case of c = 1 u wud obtain a function of f(x) rather than f(x,y). You also must take the boundaries into account when considering the domain and range of your f(x). I hope this clears the problem up for you.