Solving Partial Derivatives & Symmetry Problems: A Practice Test

[StonedPanda]

8. Let f : R^3 → R a function all whose first order partial derivatives are continuous and such that f(0, 1, 1) = 0,
f_x(0, 1, 1) = 1, f_y(0, 1, 1) = 2, f_z(0, 1, 1) = 3. Find lim
t-->0
f(t2, cosh t, et)
f(t, cos t, cosh t)

9. Let f : R2 → R such that f(x, y) = f(y,−x) for all (x, y) ∈ R2, and f(2, y) = 2 + |y|. Then
A f_x(1, 2) = 1
B f_x(1, 2) = 0
C f_x(0, 2) = 1
D f_x(0, 2) = −1
E none of these

Hey. These are two problems on a practise test. I have no clue whatsoever how to do the first. My question for the second: does f(x,y) mean the same thing as f(y,x)?

Thanks so much.

 

[James R]

When you see f(x,y)=f(y,-x), the x and y are place holders.

For example, this statement says that

f(1,2) = f(2,-1)
f(3,-1) = f(-1,-3)

etc.

So, what does f(2,y) = 2 + |y| tell you, when combined with f(x,y)=f(y,-x)?

 

[StonedPanda]

ok, that's what i thought after working with the problem for a bit. so is the answer "b" because you get a function of y?