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- Politecnico di Milano
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- Mathematical Engineering
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- Analisi Matematica II
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- Exercises · By topic
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ExercisesBy topic
Funzioni implicite
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Analisi Matematica IIBy topic
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ESERCIZI FUNZIONI IMPLICITE Dopo aver mostrato che ciascuna delle seguenti equazioniF (x,y ) = 0 definisce implicitamente un’uni- ca funzioney =φ(x), determinarne: dominio, regolarit` a, segno, segno della derivata prima, eventuali estremanti, limiti ed eventuali asintoti. Tracciarne inoltre un grafico qualitativo. a) F (x,y ) =x3 logy + 3ey+√x. b) F (x,y ) =x2yex +y3 −e−y. c) F (x,y ) =y + 4x − log(x − logy). d) F (x,y ) = (y − 2)ex + (4x2 + 3) logy. e) F (x,y ) =exy − logx +y = 0. 1
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