Let r > 0, (a, b) R2, f: Br(a, b) R, and suppose that the first-order partial
Question:
a) Set Î(h) = f(a + h, b + h) - f(a + h, b) - f(a, b + h) + f(a, b) and prove for h sufficiently small that
for some t (0, 1).
b) Prove that
c) Prove that
Transcribed Image Text:
A(h) lab+ th)-ya.b)-V,la.b) (h, th) (f,a, bth) f(a, b) -Vfy(a, b 0, th+hfyx (a, b) Δ(11) 2 Fyx (a, b). lim as-av (a , b) = a vax (a, b). dx dy
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a By the onedimensional Mean Value Theorem h hf y a h b th hf y a b th for some t ...View the full answer
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