Study -{ 0 f(x) = xy(y-ix) x6+y for z 0, = 0. for z =...

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Study -{ 0 f(x) = x³y(y-ix) x6+y² for z ‡ 0, = 0. for z = Show that even though [ƒ(z) — ƒ(0)]/z → 0 as z → 0 for any straight line through the origin, f(z) is nevertheless not complex differentiable at z = 0. Hint: play around with curves given by cubic equations. Study -{ 0 f(x) = x³y(y-ix) x6+y² for z ‡ 0, = 0. for z = Show that even though [ƒ(z) — ƒ(0)]/z → 0 as z → 0 for any straight line through the origin, f(z) is nevertheless not complex differentiable at z = 0. Hint: play around with curves given by cubic equations.

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Lim Ifzfz 0 Izz 0 0 as z0 z0 fz x3 yyixx6y2 for z not eq... View the full answer