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- University
- Politecnico di Milano
- Degree programme
- Computer Engineering
- Subject
- Analisi Matematica 1
- Academic year
- 2009-2010
- Classification
- Exam · Second midterm
- Content
- Exam paper only
- Original format
- Text
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ExamSecond midtermExam paper only
27 01 10
Study material for Analisi Matematica 1, shared by the Studwiz community and reviewed by moderators.
Analisi Matematica 1Second midterm
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ANALISI MATEMATICA 1 allievi Informatici-Telecomunicazioni seconda prova in itinere 27/01/10 1)( 6 punti) Studiare la seguente funzione f(x)/u003dx2 x /u002b1 ex//ue0a2x/u002b1/ue0a3 a) insieme di definizione e segno della funzione insieme di definizione:x /u2260 /u22121 f(x)/u003e0 per x /u003e-1 b)limiti agli estremi dell’insieme di definizione ed eventuali asintoti lim x/u2192/u2212/u221ef/ue0a2x/ue0a3/u003d/u2212/u221elim x/u2192/u002b/u221ef/ue0a2x/ue0a3/u003d /u002b/u221e lim x/u2192/u22121/u2212f/ue0a2x/ue0a3/u003d/u2212/u221elim x/u2192/u22121/u002bf/ue0a2x/ue0a3/u003d0 lim x/u2192/u2212/u221e f/ue0a2x/ue0a3 x /u003de lim x/u2192/u2212/u221ef/ue0a2x/ue0a3/u2212ex /u003d/u2212/u221e lim x/u2192/u002b/u221e f/ue0a2x/ue0a3 x /u003de lim x/u2192/u2212/u221ef/ue0a2x/ue0a3/u2212ex /u003de npon esistono asintoti obliqui c)calcolo e studio di f’(x) f’(x)/u003dxe x//ue0a2x/u002b1/ue0a3/ue0a2x2 /u002b4x /u002b2/ue0a3 /ue0a2x /u002b1/ue0a33 T’/u003dT f’(x)/u22650 per 0 /u2264x /u22642- 2 x/u22652 /u002b2 lim x/u2192/u22121/u2212f/u2032/ue0a2x/ue0a3/u003d /u002b/u221e d) eventuali massimi e minimi relativi e assoluti x/u003d0 punto di minimo relativo x/u003d2- 2 punto di massimo relativo x/u003d2/u002b2 punto di minimo relativo e) grafico ________________________________________________________ 2) (4 punti) Risolvere la seguente equazione nel campo complesso (|z /u22126i| /u2212|z /u002b4i|/ue0a3/ue0a2z3 /u22121/ue0a3/u003d0 z3 /u003d1 z 1 /u003d1, z 2 /u003dei2/u03c0/3, z3 /u003dei4/u03c0/3 Posto z/u003dx/u002biy si ha |x /u002biy /u22126i| /u003d|x /u002biy /u002b4i| x2 /u002b/ue0a2y /u22126/ue0a32 /u003dx2 /u002b/ue0a2y /u002b4/ue0a32 36-12y/u003d16/u002b8y y/u003d1 /u2200x _____________________________________________________________________________ 3)(2 punti)…
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