Fusco Marcellini Sbordone Analisi Matematica 2 Esercizi Pdf 77 Exclusive Jun 2026

You could write:

This expression depends on ( \theta ), not just ( r ). For ( \theta = \pi/4 ), we get ( -(\frac12)(\sqrt2) \neq 0 ). Hence the limit does not exist (fails to be 0). So ( f ) is at ( (0,0) ), despite having partial derivatives. You could write: This expression depends on (

: This includes topics like line integrals, surface integrals, and vector fields, essential for physics and engineering. So ( f ) is at ( (0,0) ), despite having partial derivatives

Such exercises on page 77 would serve as a bridge to later chapters on , C¹ implies differentiability (here ( f \notin C^1 )), and Schwarz theorem (here mixed partials at origin: compute ( f_xy(0,0) ) would show symmetry? Actually ( f_xy ) and ( f_yx ) differ — another typical advanced exercise). Actually ( f_xy ) and ( f_yx )

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