- #1

- 289

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It would be easy to prove that it's differentiable at (0,0), but differentiable at any point...it just doesnt seem to simplify.

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- Thread starter tmc
- Start date

- #1

- 289

- 1

It would be easy to prove that it's differentiable at (0,0), but differentiable at any point...it just doesnt seem to simplify.

- #2

matt grime

Science Advisor

Homework Helper

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f_y= -2x

you can show that is a continuous function of x,y with epsilons and deltas, right?

- #3

- 289

- 1

[tex]\[

\mathop {\lim }\limits_{\left( {x,y} \right) \to \left( {x_0 ,y_0 } \right)} \frac{{\left\| {f\left( {x,y} \right) - f\left( {x_0 ,y_0 } \right) - D_f \left( {x_0 ,y_0 } \right) \cdot \left( {x - x_0 ,y - y_0 } \right)} \right\|}}{{\left\| {\left( {x - x_0 ,y - y_0 } \right)} \right\|}} = 0

\]

[/tex]

which is where im having some problems.

Obviously, yes it would be easy to simply prove that it is C1, which in turn would imply differentiability...

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