Topic 2. Differentiability. (a) Describe the basic theory of differentiability for functions R2 → R, including partial and directional derivatives, gradient, differentia- bility and continuous differentiability. Highlight the differences with respect to R. v (b) Use the function (x, y) # (0,0), (r, y) = (0,0) f(r, y) = to illustrate the theory in (a), especially with respect to properties at, and in a vicinity of, the two different points (1, 1) and (0,0). Kindly explain (use) f cxY) according to pars @ aT the given poinis
Topic 2. Differentiability. (a) Describe the basic theory of differentiability for functions R2 → R, including partial and directional derivatives, gradient, differentia- bility and continuous differentiability. Highlight the differences with respect to R. v (b) Use the function (x, y) # (0,0), (r, y) = (0,0) f(r, y) = to illustrate the theory in (a), especially with respect to properties at, and in a vicinity of, the two different points (1, 1) and (0,0). Kindly explain (use) f cxY) according to pars @ aT the given poinis
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Topic 2. Differentiability.
(a) Describe the basic theory of differentiability for functions R? → R,
including partial and directional derivatives, gradient, differentia-
bility and continuous differentiability. Highlight the differences
with respect to R.
x (b) Use the function
(x, y) # (0,0),
(x, y) = (0,0)
f (x, y) =
x² +y? >
0,
to illustrate the theory in (a), especially with respect to properties
at, and in a vicinity of, the two different points (1, 1) and (0,0).
1-
Kindlly explain (use) f cxiY)
according tO Pars a) aT
the given poinTs
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