Taylor's Theorem

*cricket cricket*

*waits for Rust or Corn*

I was thinking of Noah. Maybe Russt might know, but I think Corn is still studying single-variable calculus.

it doesn't? (equations 7.5 / 7.6)

For (7.5), they have f''(a)(x-a)^2+f'(a)f'(b)(x-a)(y-b)+f''(b)(y-b)^2. There should be a coefficient of 2 in the middle term. They do something similar for (7.6). I'm not sure why they left the coefficients out.

Hmm... doesn't that run into the same problem as mine? That gives me an idea though:



How would I express this for variables? In the notation I used in the first post, I can just add a (z-z0)(d/dz) term inside the brackets without losing anything, but I don't think I can do the same thing here. For example, if I did use this notation, if a=x-x0, b=y-y0, and c=z-z0, I would lose the 6abc term the expansion of (a+b+c)^3. Or am I supposed to lose that term?