- #1

2sin54

- 109

- 1

[tex]\lim_{x\to0} \left[\frac{d}{dy} \frac{d}{dx} f(x,y)\right] = \frac{d}{dy} \left[\lim_{x\to0} \frac{d}{dx} f(x,y)\right][/tex]

holds true for all

*f(x,y).*Thanks.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- I
- Thread starter 2sin54
- Start date

- #1

2sin54

- 109

- 1

[tex]\lim_{x\to0} \left[\frac{d}{dy} \frac{d}{dx} f(x,y)\right] = \frac{d}{dy} \left[\lim_{x\to0} \frac{d}{dx} f(x,y)\right][/tex]

holds true for all

- #2

jedishrfu

Mentor

- 14,077

- 8,031

http://www.math.ucsd.edu/~mradclif/teaching/Math10C/LectureNotes/second_order_partial_derivatives.pdf

Are you trying to prove this?

- #3

2sin54

- 109

- 1

No, not exactly. My f(x,y) is a huge compound function and it's a hassle to differentiate with respect to both variables and then take the limit, as opposed to differentiating by x, setting the limit and then differentiating (the now simpler function) by y.

http://www.math.ucsd.edu/~mradclif/teaching/Math10C/LectureNotes/second_order_partial_derivatives.pdf

Are you trying to prove this?

Share:

- Last Post

- Replies
- 29

- Views
- 508

- Last Post

- Replies
- 7

- Views
- 526

- Replies
- 4

- Views
- 435

- Last Post

- Replies
- 11

- Views
- 583

- Last Post

- Replies
- 2

- Views
- 104

- Replies
- 1

- Views
- 466

- Last Post

- Replies
- 8

- Views
- 396

- Last Post

- Replies
- 3

- Views
- 404

- Last Post

- Replies
- 3

- Views
- 576

MHB
Find limit

- Last Post

- Replies
- 3

- Views
- 608