Question

HELP!!!!!!! f(x,y)=x/(x^2+y^2), a) find an equation of the level curve which contains point P (1,1). b)find a normal vector to the level curve found in part a at point P

Answer 1

first plug in x=1,y=1 to get constant value
f(x,y) = 1/2

level curve
\[\frac{x}{x^2 +y^2} = \frac{1}{2}\]
this can be rewritten as a circle
\[(x-1)^2 +y^2 = 1\]

From diagram you can see that the normal vector is going at straight up
N <0,1>

Answer 2

Thanks