5xy sin ³²x + 3y² 0, f(x, y) (a) Prove that lim T if (x,y) + (0,0) if (x,y) = (0,0) f(x,y) does not exist. (x,y) = (0,0) b) Deturmine if f is differentiable at (0,0)? Explain why or why not.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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5xy
sin ³²x + 3y²
f(x, y)
0,
(a) Prove that lim
; if (x,y) + (0,0)
if (x,y) = (0,0)
f(x,y) does not exist.
(x,y) = (0,0)
3) Determine if f is differentiable at (0,0)?
Explain why or why not.
Transcribed Image Text:5xy sin ³²x + 3y² f(x, y) 0, (a) Prove that lim ; if (x,y) + (0,0) if (x,y) = (0,0) f(x,y) does not exist. (x,y) = (0,0) 3) Determine if f is differentiable at (0,0)? Explain why or why not.
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