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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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 48CR
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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
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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