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xy log(x² + y²), (x,y) # ɔ, (x,y) =

xy log(x² + y²), (x,y) # ɔ, (x,y) =

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 36CR
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Question

a) Is the function continuous at (0,0)?

b) Do the partial derivatives (D₁f)(0,0) and (D₂f)(0,0) exist?

c) For which u in ℝ² \ {0} does the directional derivative (D_uf)(0,0) exist?

d) Is f differentiable at (0,0)?

e) Determine the partial derivatives D₁f(x,y) and D₂f(x,y) for (x,y) ≠ (0,0).

f) Is f a C¹ function?


HINT: use the following standerd limit: see picture.

You could either solve these questions, or a detailed explanation

Thank you!

xylog(x² + y²), (x,y) ± (0,0), f(x,y) := 0, (x, y) = (0,0).
Transcribed Image Text:xylog(x² + y²), (x,y) ± (0,0), f(x,y) := 0, (x, y) = (0,0).
lim sa log s = 0, Va > 0 80
Transcribed Image Text:lim sa log s = 0, Va > 0 80
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