I have:

http://img12.imageshack.us/img12/6121/capturerhf.png

Is the function differentiable in (0,2)? If so, find its Tangent Plane.

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- December 13th 2011, 01:10 PMGIPCIs the following function differentiable?
I have:

http://img12.imageshack.us/img12/6121/capturerhf.png

Is the function differentiable in (0,2)? If so, find its Tangent Plane. - December 13th 2011, 02:43 PMFernandoRevillaRe: Is the following function differentiable?
We have , so

**if**is differentiable at the only possible differential is . Now, analyze if . - December 14th 2011, 03:08 AMGIPCRe: Is the following function differentiable?
I came to that lim term myself and that's where I kind of get stuck with all the epsilons. I can't draw a concrete conclusion from there if it is indeed 0 or just a small epsilon bigger than 0. That's what making this exercise difficult.

- December 14th 2011, 03:49 AMFernandoRevillaRe: Is the following function differentiable?
Use in a neighborhood of in the precise terms of the Taylor's formula.

- December 14th 2011, 06:35 AMGIPCRe: Is the following function differentiable?
I came to a conclusion that the function is indeed differentiable, but I have to show a strict rigorous proof.

How do I expand f to its Taylor Series?

And from there, how do I find the tangent plane? - December 14th 2011, 10:29 AMFernandoRevillaRe: Is the following function differentiable?
That is a correct conclusion.

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but I have to show a strict rigorous proof.

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How do I expand f to its Taylor Series?

Quote:

And from there, how do I find the tangent plane?

- December 14th 2011, 10:38 AMGIPCRe: Is the following function differentiable?
Sorry for the follow up questions. Even with the Taylor expansion, how do I use it in the lim term you prescribed earlier?

And also, after i prove differentiability, how do I find the appropriate P0 to plug into the formula for the tangent plane?

I'm sorry for asking pathetic questions :(