Consider the function f(x, y) =(a) Find f(0, 0) and f(0, 0)fx(0, 0)fy(o, 0)=(b) Determine the points (if any) at which f(x, y) or fy(x, y) fails to existf(x, y) and f(x, y) fail to exist for y -x1/5, x 0.O f(x, y) and f(x, y) always exist.Of(x, y) and fx, y) fail to exist for y x, x # 0f(x, y) and f(x, y) fail to exist for y x1/5, x * 0.f(x, y) and f (x, y) fail to exist for y0.-x, x

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Asked Oct 21, 2019
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Consider the function f(x, y) =
(a) Find f(0, 0) and f(0, 0)
fx(0, 0)
fy(o, 0)=
(b) Determine the points (if any) at which f(x, y) or fy(x, y) fails to exist
f(x, y) and f(x, y) fail to exist for y -x1/5, x 0.
O f(x, y) and f(x, y) always exist.
Of(x, y) and fx, y) fail to exist for y x, x # 0
f(x, y) and f(x, y) fail to exist for y x1/5, x * 0.
f(x, y) and f (x, y) fail to exist for y
0.
-x, x
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Consider the function f(x, y) = (a) Find f(0, 0) and f(0, 0) fx(0, 0) fy(o, 0)= (b) Determine the points (if any) at which f(x, y) or fy(x, y) fails to exist f(x, y) and f(x, y) fail to exist for y -x1/5, x 0. O f(x, y) and f(x, y) always exist. Of(x, y) and fx, y) fail to exist for y x, x # 0 f(x, y) and f(x, y) fail to exist for y x1/5, x * 0. f(x, y) and f (x, y) fail to exist for y 0. -x, x

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Expert Answer

Step 1

According to the given information the given function is:

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S(,y)-( +y'

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Step 2

For part (a)

First find fx and fy

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(x,y)(x+y 1 f.(x.y) +y5x (x, y) (x+y') similarly S(x, y) (x +y°)

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Step 3

Now find fx(0,0) and fy(0,0):

...
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(0,0) (0,0)-0 (x+y' (0,0) =0 (x+y') (0,0)=

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Math

Calculus