1.a PROVA DE SMA301-CALCULO I - Professor Alexandre 3 ......1.a PROVA DE SMA301-CALCULO I -...

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1.a PROVA DE SMA301-C ´ ALCULO I - Professor Alexandre 3.04.2013 - A NOME: N. o USP: NOTA: Quest˜ ao Resposta Valor Quest˜ ao Resposta Valor 1. a (a) (b) (c) (d) (e) 6. a (a) (b) (c) (d) (e) 2. a (a) (b) (c) (d) (e) 7. a (a) (b) (c) (d) (e) 3. a (a) (b) (c) (d) (e) 8. a (a) (b) (c) (d) (e) 4. a (a) (b) (c) (d) (e) 9. a (a) (b) (c) (d) (e) 5.a (a) (b) (c) (d) (e) 10. a (a) (b) (c) (d) (e) Regras: 1- ´ UNICA SEM RASURA 2- 1. a Quest˜ ao (Valor 1.0): f : R ! R f(x) := (3x) x 2 R (a) 3(b) 2(c) 3 2 (d) 2 3 (e) 2. a Quest˜ ao (Valor 1.0): f : h - 2 , 2 i ! [-1, 1] f(x) := (2x) x 2 R (a) (b) (c) (d) (e) 3. a Quest˜ ao (Valor 1.0): a, b c, d (a) a + b c + d (b) a.b a + c (c) a + b a + c (d) a + b c + d (e) a.b c.d 4. a Quest˜ ao (Valor 1.0): A = { 1 n + 1 m : m, n 2 N } (a) (A)= 0 (A)= 2 B = { 1 j : j 2 N } [ {0} A (b) (A)= 0 (A)= 1 B = { 1 j : j 2 N } [ {0} A (c) (A)= 0 (A)= 2 B = { 1 j : j 2 N } A (d) (A)= 0 (A)= 2 B =[0, 2] A (e) (A)= 0 (A)= 1 B =[0, 1] A 5. a Quest˜ ao (Valor 1.0): f : R ! R f(x) . = x 2 - 4 x 2 R (a) f Ox f [-4, 1) (b) f f [-4, 1) (c) f Oy f [4, 1) (d) f Ox f [-4, 1) (e) f Oy f [-4, 1)

Transcript of 1.a PROVA DE SMA301-CALCULO I - Professor Alexandre 3 ......1.a PROVA DE SMA301-CALCULO I -...

  • 1.a PROVA DE SMA301-CÁLCULO I - Professor Alexandre 3.04.2013 - A

    NOME: N.o USP: NOTA:

    Questão Resposta Valor Questão Resposta Valor

    1.a (a) (b) (c) (d) (e) 6.a (a) (b) (c) (d) (e)

    2.a (a) (b) (c) (d) (e) 7.a (a) (b) (c) (d) (e)

    3.a (a) (b) (c) (d) (e) 8.a (a) (b) (c) (d) (e)

    4.a (a) (b) (c) (d) (e) 9.a (a) (b) (c) (d) (e)

    5.a (a) (b) (c) (d) (e) 10.a (a) (b) (c) (d) (e)

    Regras: 1 - ÚNICA SEM RASURA

    2 -

    1.a Questão (Valor 1.0): f : R ! R f(x) := (3x) x 2 R(a) 3⇡

    (b) 2⇡

    (c)3

    2⇡

    (d)2

    3⇡

    (e)

    2.a Questão (Valor 1.0): f :h-⇡

    2,⇡

    2

    i! [-1, 1] f(x) := (2x) x 2 R

    (a)

    (b)

    (c)

    (d)

    (e)

    3.a Questão (Valor 1.0): a, b c, d

    (a) a+ b c+ d

    (b) a.b a+ c

    (c) a+ b a+ c

    (d) a+ b c+ d

    (e) a.b c.d

    4.a Questão (Valor 1.0): A = { 1n +1m : m,n 2 N

    ⇤}

    (a) (A) = 0 (A) = 2 B = { 1j : j 2 N⇤} [ {0} A

    (b) (A) = 0 (A) = 1 B = { 1j : j 2 N⇤} [ {0} A

    (c) (A) = 0 (A) = 2 B = { 1j : j 2 N⇤} A

    (d) (A) = 0 (A) = 2 B = [0, 2] A

    (e) (A) = 0 (A) = 1 B = [0, 1] A

    5.a Questão (Valor 1.0): f : R ! R f(x) .= x2 - 4 x 2 R(a) f Ox f [-4,1)(b) f f [-4,1)(c) f Oy f [4,1)(d) f Ox f [-4,1)(e) f Oy f [-4,1)

  • 6.a Questão (Valor 1.0): x 2⇣-⇡

    2,⇡

    2

    (a) | (x)| > |x| > | (x)| (b) | (x)| |x| |x| > | (x)|(c) | (x)| > |x| |x| | (x)| (d) | (x)| |x| | (x)|(e) | (x)| |x| | (x)|

    7.a Questão (Valor 1.0): |x- 2| = |2x- 6|

    (a)

    �-4,-

    8

    3

    �(b)

    �4,-

    8

    3

    (c)

    �4,

    8

    3

    �(d)

    �-4,

    8

    3

    (e)

    8.a Questão (Valor 1.0): |1- 3x| 5

    (a)

    4

    3, 2

    �(b)

    -2,

    4

    3

    (c)

    -2,-

    4

    3

    �(d)

    (e)

    -4

    3, 2

    9.a Questão (Valor 1.0): A⇢R { n :n2Z}⇢A(a) A sup A inf (A) A

    (b) A sup A inf (A) A

    (c) A sup A inf

    (d) A sup A inf (A) � 1 (A) = -1(e) A sup A inf (A) -1 (A) = 1

    10.a Questão (Valor 1.0):

    OPQR

    OP = 10 PQ = QR = 5

    S OP

    x.= OS A

    x A = A(x)SO

    R Q

    P

    x� -

    (a) A(x) =1

    2x2 , x 2 [0, 10] (b) A(x) =

    8><

    >:

    1

    2x2 , x 2 [0, 5]

    5x-25

    2, x 2 [5, 10]

    (c) A(x) = 5x-25

    2, x 2 [0, 10] (d) A(x) =

    8><

    >:

    5x-25

    2, x 2 [0, 5]

    1

    2x2 , x 2 [5, 10]

    (e) A(x) =75

    2, x 2 [0, 10]

    BOA PROVA!

  • 1.a PROVA DE SMA301-CÁLCULO I - Professor Alexandre 3.04.2013 - B

    NOME: N.o USP: NOTA:

    Questão Resposta Valor Questão Resposta Valor

    1.a (a) (b) (c) (d) (e) 6.a (a) (b) (c) (d) (e)

    2.a (a) (b) (c) (d) (e) 7.a (a) (b) (c) (d) (e)

    3.a (a) (b) (c) (d) (e) 8.a (a) (b) (c) (d) (e)

    4.a (a) (b) (c) (d) (e) 9.a (a) (b) (c) (d) (e)

    5.a (a) (b) (c) (d) (e) 10.a (a) (b) (c) (d) (e)

    Regras: 1 - ÚNICA SEM RASURA

    2 -

    1.a Questão (Valor 1.0): f : R ! R f(x) := (3x) x 2 R(a) 2⇡

    (b)3

    2⇡

    (c)2

    3⇡

    (d) 3⇡

    (e)

    2.a Questão (Valor 1.0): f :h-⇡

    2,⇡

    2

    i! [-1, 1] f(x) := (2x) x 2 R

    (a)

    (b)

    (c)

    (d)

    (e)

    3.a Questão (Valor 1.0): a, b c, d

    (a) a.b c.d

    (b) a+ b c+ d

    (c) a.b a+ c

    (d) a+ b a+ c

    (e) a+ b c+ d

    4.a Questão (Valor 1.0): A = { 1n +1m : m,n 2 N

    ⇤}

    (a) (A) = 0 (A) = 1 B = [0, 1] A

    (b) (A) = 0 (A) = 2 B = { 1j : j 2 N⇤} [ {0} A

    (c) (A) = 0 (A) = 1 B = { 1j : j 2 N⇤} [ {0} A

    (d) (A) = 0 (A) = 2 B = { 1j : j 2 N⇤} A

    (e) (A) = 0 (A) = 2 B = [0, 2] A

    5.a Questão (Valor 1.0): f : R ! R f(x) .= x2 - 4 x 2 R(a) f Ox f [-4,1)(b) f f [-4,1)(c) f Oy f [4,1)(d) f Ox f [-4,1)(e) f Oy f [-4,1)

  • 6.a Questão (Valor 1.0): x 2⇣-⇡

    2,⇡

    2

    (a) | (x)| |x| | (x)| (b) | (x)| |x| |x| > | (x)|(c) | (x)| > |x| |x| | (x)| (d) | (x)| |x| | (x)|(e) | (x)| > |x| > | (x)|

    7.a Questão (Valor 1.0): |x- 2| = |2x- 6|

    (a)

    �4,

    8

    3

    �(b)

    �-4,

    8

    3

    (c)

    �-4,-

    8

    3

    �(d)

    �4,-

    8

    3

    (e)

    8.a Questão (Valor 1.0): |1- 3x| 5

    (a)

    4

    3, 2

    �(b)

    -2,

    4

    3

    (c)

    -4

    3, 2

    �(d)

    (e)

    -2,-

    4

    3

    9.a Questão (Valor 1.0): A⇢R { n :n2Z}⇢A(a) A sup A inf (A) A

    (b) A sup A inf

    (c) A sup A inf (A) A

    (d) A sup A inf (A) � 1 (A) = -1(e) A sup A inf (A) -1 (A) = 1

    10.a Questão (Valor 1.0):

    OPQR

    OP = 10 PQ = QR = 5

    S OP

    x.= OS A

    x A = A(x)SO

    R Q

    P

    x� -

    (a) A(x) =1

    2x2 , x 2 [0, 10] (b) A(x) =

    8><

    >:

    1

    2x2 , x 2 [0, 5]

    5x-25

    2, x 2 [5, 10]

    (c) A(x) = 5x-25

    2, x 2 [0, 10] (d) A(x) =

    8><

    >:

    5x-25

    2, x 2 [0, 5]

    1

    2x2 , x 2 [5, 10]

    (e) A(x) =75

    2, x 2 [0, 10]

    BOA PROVA!

  • 1.a PROVA DE SMA301-CÁLCULO I - Professor Alexandre 3.04.2013 - C

    NOME: N.o USP: NOTA:

    Questão Resposta Valor Questão Resposta Valor

    1.a (a) (b) (c) (d) (e) 6.a (a) (b) (c) (d) (e)

    2.a (a) (b) (c) (d) (e) 7.a (a) (b) (c) (d) (e)

    3.a (a) (b) (c) (d) (e) 8.a (a) (b) (c) (d) (e)

    4.a (a) (b) (c) (d) (e) 9.a (a) (b) (c) (d) (e)

    5.a (a) (b) (c) (d) (e) 10.a (a) (b) (c) (d) (e)

    Regras: 1 - ÚNICA SEM RASURA

    2 -

    1.a Questão (Valor 1.0): f :h-⇡

    2,⇡

    2

    i! [-1, 1] f(x) := (2x) x 2 R

    (a)

    (b)

    (c)

    (d)

    (e)

    2.a Questão (Valor 1.0): f : R ! R f(x) := (3x) x 2 R(a) 2⇡

    (b)3

    2⇡

    (c)2

    3⇡

    (d) 3⇡

    (e)

    3.a Questão (Valor 1.0): A = { 1n +1m : m,n 2 N

    ⇤}

    (a) (A) = 0 (A) = 1 B = [0, 1] A

    (b) (A) = 0 (A) = 2 B = { 1j : j 2 N⇤} [ {0} A

    (c) (A) = 0 (A) = 1 B = { 1j : j 2 N⇤} [ {0} A

    (d) (A) = 0 (A) = 2 B = { 1j : j 2 N⇤} A

    (e) (A) = 0 (A) = 2 B = [0, 2] A

    4.a Questão (Valor 1.0): a, b c, d

    (a) a.b c.d

    (b) a+ b c+ d

    (c) a.b a+ c

    (d) a+ b a+ c

    (e) a+ b c+ d

    5.a Questão (Valor 1.0): f : R ! R f(x) .= x2 - 4 x 2 R(a) f Ox f [-4,1)(b) f f [-4,1)(c) f Oy f [4,1)(d) f Ox f [-4,1)(e) f Oy f [-4,1)

  • 6.a Questão (Valor 1.0): |1- 3x| 5

    (a)

    4

    3, 2

    �(b)

    -2,

    4

    3

    (c)

    -4

    3, 2

    �(d)

    (e)

    -2,-

    4

    3

    7.a Questão (Valor 1.0): x 2⇣-⇡

    2,⇡

    2

    (a) | (x)| |x| | (x)| (b) | (x)| |x| |x| > | (x)|(c) | (x)| > |x| |x| | (x)| (d) | (x)| |x| | (x)|(e) | (x)| > |x| > | (x)|

    8.a Questão (Valor 1.0): A⇢R { n :n2Z}⇢A(a) A sup A inf (A) A

    (b) A sup A inf

    (c) A sup A inf (A) A

    (d) A sup A inf (A) � 1 (A) = -1(e) A sup A inf (A) -1 (A) = 1

    9.a Questão (Valor 1.0): |x- 2| = |2x- 6|

    (a)

    �4,

    8

    3

    �(b)

    �-4,

    8

    3

    (c)

    �-4,-

    8

    3

    �(d)

    �4,-

    8

    3

    (e)

    10.a Questão (Valor 1.0):

    OPQR

    OP = 10 PQ = QR = 5

    S OP

    x.= OS A

    x A = A(x)SO

    R Q

    P

    x� -

    (a) A(x) =1

    2x2 , x 2 [0, 10] (b) A(x) =

    8><

    >:

    1

    2x2 , x 2 [0, 5]

    5x-25

    2, x 2 [5, 10]

    (c) A(x) = 5x-25

    2, x 2 [0, 10] (d) A(x) =

    8><

    >:

    5x-25

    2, x 2 [0, 5]

    1

    2x2 , x 2 [5, 10]

    (e) A(x) =75

    2, x 2 [0, 10]

    BOA PROVA!

  • 1.a PROVA DE SMA301-CÁLCULO I - Professor Alexandre 3.04.2013 - D

    NOME: N.o USP: NOTA:

    Questão Resposta Valor Questão Resposta Valor

    1.a (a) (b) (c) (d) (e) 6.a (a) (b) (c) (d) (e)

    2.a (a) (b) (c) (d) (e) 7.a (a) (b) (c) (d) (e)

    3.a (a) (b) (c) (d) (e) 8.a (a) (b) (c) (d) (e)

    4.a (a) (b) (c) (d) (e) 9.a (a) (b) (c) (d) (e)

    5.a (a) (b) (c) (d) (e) 10.a (a) (b) (c) (d) (e)

    Regras: 1 - ÚNICA SEM RASURA

    2 -

    1.a Questão (Valor 1.0): x 2⇣-⇡

    2,⇡

    2

    (a) | (x)| > |x| > | (x)| (b) | (x)| |x| |x| > | (x)|(c) | (x)| > |x| |x| | (x)| (d) | (x)| |x| | (x)|(e) | (x)| |x| | (x)|

    2.a Questão (Valor 1.0): |x- 2| = |2x- 6|

    (a)

    �-4,-

    8

    3

    �(b)

    �4,-

    8

    3

    (c)

    �4,

    8

    3

    �(d)

    �-4,

    8

    3

    (e)

    3.a Questão (Valor 1.0): |1- 3x| 5

    (a)

    4

    3, 2

    �(b)

    -2,

    4

    3

    (c)

    -2,-

    4

    3

    �(d)

    (e)

    -4

    3, 2

    4.a Questão (Valor 1.0): A⇢R { n :n2Z}⇢A(a) A sup A inf (A) A

    (b) A sup A inf (A) A

    (c) A sup A inf

    (d) A sup A inf (A) � 1 (A) = -1(e) A sup A inf (A) -1 (A) = 1

    5.a Questão (Valor 1.0): f : R ! R f(x) := (3x) x 2 R(a) 3⇡

    (b) 2⇡

    (c)3

    2⇡

    (d)2

    3⇡

    (e)

  • 6.a Questão (Valor 1.0):

    OPQR

    OP = 10 PQ = QR = 5

    S OP

    x.= OS A

    x A = A(x)SO

    R Q

    P

    x� -

    (a) A(x) =1

    2x2 , x 2 [0, 10] (b) A(x) =

    8><

    >:

    1

    2x2 , x 2 [0, 5]

    5x-25

    2, x 2 [5, 10]

    (c) A(x) = 5x-25

    2, x 2 [0, 10] (d) A(x) =

    8><

    >:

    5x-25

    2, x 2 [0, 5]

    1

    2x2 , x 2 [5, 10]

    (e) A(x) =75

    2, x 2 [0, 10]

    7.a Questão (Valor 1.0): f :h-⇡

    2,⇡

    2

    i! [-1, 1] f(x) := (2x) x 2 R

    (a)

    (b)

    (c)

    (d)

    (e)

    8.a Questão (Valor 1.0): a, b c, d

    (a) a+ b c+ d

    (b) a.b a+ c

    (c) a+ b a+ c

    (d) a+ b c+ d

    (e) a.b c.d

    9.a Questão (Valor 1.0): A = { 1n +1m : m,n 2 N

    ⇤}

    (a) (A) = 0 (A) = 2 B = { 1j : j 2 N⇤} [ {0} A

    (b) (A) = 0 (A) = 1 B = { 1j : j 2 N⇤} [ {0} A

    (c) (A) = 0 (A) = 2 B = { 1j : j 2 N⇤} A

    (d) (A) = 0 (A) = 2 B = [0, 2] A

    (e) (A) = 0 (A) = 1 B = [0, 1] A

    10.a Questão (Valor 1.0): f : R ! R f(x) .= x2 - 4 x 2 R(a) f Ox f [-4,1)(b) f f [-4,1)(c) f Oy f [4,1)(d) f Ox f [-4,1)(e) f Oy f [-4,1)

    BOA PROVA!