Question

PLEASE HELP!!!! calc three topic... finding the partial derivatives at a point where the limit is undefined.

Answer 1

It is problem two on the pdf. I have no clue.

Answer 2

Which part of problem two?

Answer 3

part b

Answer 4

Okay.
\[ f_x(0,0) = \lim_{\Delta x \rightarrow 0} \frac{f(\Delta x,0) - f(0,0)}{\Delta x} \]
what are \[ f(\Delta x,0) \text{ and }f(0,0)?\]

Answer 5

I have no clue

Answer 6

Just plug those values in.

Answer 7

I don't understand

Answer 8

f(x,y) is defined for you. if you want f(0,0), plug 0 in for x and 0 in for y. etc.

Answer 9

ok if I plug in zero for x and zero for y then I get zero over zero

Answer 10

You'll notice that f(x,y) is defined piecewisely, and in fact (0,0) is perfectly well-defined.

Answer 11

I still don't get it..... are you saying that for f(0,0) plug in zero? Then what about delta x?

Answer 12

I'm saying that if you look at the definition of f(x,y), it explicitly says "if (x,y) = 0, then f(x,y) = 0". For f(delta x,0), plug in zero for y and delta x for x.

Answer 13

sorry,
"if (x,y) = (0,0) .."

Answer 14

ok it says that delta x approaches zero so do you just plug that in for delta x?

Answer 15

Well actually, you'll notice that if y =0, the whole thing is zero so it doesn't much matter.

Answer 16

I really don't feel like that is correct, but honestly I can't get anyone to EXPLAIN this so I don't really know

Answer 17

so your just saying it is zero?

Answer 18

Yeah, it's zero. Clearly that function is zero if x = 0 and if y = 0, right? So if you walk along the axes, the limit is always going to be zero.

Answer 19

What's bothering you about that?

Answer 20

Nevermind thanks anyway

Answer 21

Haha alright, fair enough... do you understand it, or are you just calling it a day?