80 exercicios calculo

Upload: jardel-cardoso

Post on 04-Feb-2018

234 views

Category:

Documents


0 download

TRANSCRIPT

  • 7/21/2019 80 exercicios CALCULO

    1/12

  • 7/21/2019 80 exercicios CALCULO

    2/12

    8

    B. D#(#'%i,&' $%&'#p'#s#,(&!o p&'&%0('i*&"& '#(& 5$# p&ss& p#+ospo,(os A # / s#,"o:

    . D#(#'%i,&' $%&'#p'#s#,(&!o p&'&%0('i*&"& '#(& '#p'#s#,(&"& po':

    1.E,*o,('# #5$&@#sp&'&%0('i*&s p&'& &s '#(&s,os s#$i,(#s #-#'*)*ios:

    &2. A '#(& 5$# p&ss& p#+o

    po,(o(3, 4, 1)P

    # 0 p&'&+#+& &o

    3#(o'i j k+ +

    .

    62. A '#(& 5$# p&ss& p#+o

    po,(o

    (1, 2, 1), ( 1, 0,1)P Q

    .*2. A '#(& 5$# p&ss& p#+o po,(o

    ( 2,0,3), (3,5, 2)P Q .

    "2. A '#(& 5$# p&ss& po'

    (1, 2, 1)# 0 p#'p#,"i*$+&' &o

    p+&,o

    3 7 5 21x y z+ + =

    .

    #2. A '#(& 5$# p&ss& po'

    (0, 7, 0)# 0 p#'p#,"i*$+&' &o

    p+&,o2 2 13x y z+ + =

    .

    42. A '#(& 5$# p&ss& po'(2,3,0)

    # 0 p#'p#,"i*$+&' &os 3#(o'#s

    2 3 , 3 4 5u i j k v i j k = + + = + +.

    E,*o,('# #5$&@#s p&'& osp+&,os ,os #-#'*)*ios 111;.

    11.O p+&,o 5$# p&ss& po'

    0(0, 2, 1)P

    # 0 ,o'%&+ &

    3 2n i j k = .

    18.O p+&,o 5$# p&ss& po'

    (1, 1, 3)# 0 p&'&+#+o &o p+&,o

    3 7x y z+ + =

    .1;.O p+&,o 5$# p&ss& po'

    (1,1, 1),(2, 0,2), (0, 2,1) .

    Nos #-#'*)*ios 1=1/ #,*o,('#& "is(,*i& "o po,(o &(0 & '#(&:

    1=.(0, 0,12); 4 , 2 , 2x t y t z t= = =

    1>.

    (0, 0, 0); 5 3 , 5 4 , 3 5x t y t z t= + = + =

    1?.

    (2,1, 3); 2 2 , 1 6 , 3x t y t z= + = + =

    1.(2,1, 1); 2 , 1 2 , 2x t y t z t = = + =

    1B.D#(#'%i,&' & "#'i3&"& "&ss#$i,(#s 4$,@#s 3#(o'i&is:

  • 7/21/2019 80 exercicios CALCULO

    3/12

  • 7/21/2019 80 exercicios CALCULO

    4/12

    =

    8?.S#. Us&,"o &s p'op'i#"&"#s/*&+*$+&' os +i%i(#s s#$i,(#s:

    ;?. C&+*$+&' os s#$i,(#s +i%i(#s"# 4$,@#s *o%pos(&s:

    ;.C&+*$+&s os s#$i,(#s +i%i(#s:

    8B.

    8.

    ;.

    ;1.

  • 7/21/2019 80 exercicios CALCULO

    5/12

    >

    ;B. C&+*$+&' os s#$i,(#s +i%i(#s#,3o+3#,"o i,"#(#'%i,&@#s:

    ;. C&+*$+&' os +i%i(#s s#$i,(#s:

    =. Es*'#3#' o *o,B. V#'i*&' & '#'& "& *&"#i&

    dh f dx f dy

    dt x dt y dt

    = +

    p&'& &s4$,@#s:

    =1.

    =8.

    =;.

    ==.

    =>.

    =?.=.

    =B.

    =.

    >.

    >1.>8.

    >;.

    >=.

    >>.

    >?.

  • 7/21/2019 80 exercicios CALCULO

    6/12

    ?

    Nos #-#'*)*ios >?8/ "#(#'%i,&'

    dz

    dt/ $s&,"o & '#'& "& *&"#i&:

    ?>. V#'i*&' & '#'& "& *&"#i& p&'&&s 4$,@#s:

    Nos #-#'*)*ios ???/ "#(#'%i,&'

    &s "#'i3&"&s p&'*i&is

    z

    u

    #

    z

    v

    /$s&,"o & '#'& "& *&"#i&:

    >.

    ?.

    ?1.

    ?8.

    ?;

    ?=.

    ??.?.

    ?B.

    ?.

  • 7/21/2019 80 exercicios CALCULO

    7/12

    Nos #-#'*)*ios ;/ "#(#'%i,&'

    &s "#'i3&"&s p&'*i&is

    z

    x

    #

    z

    y

    .

    =. D#(#'%i,&' &s "#'i3&"&s

    p&'*i&is

    w

    u

    #

    w

    v

    >. C&+*$+&' o

  • 7/21/2019 80 exercicios CALCULO

    8/12

    B

    &,(#s "# "i4#'#,*i&'. D#pois/ 62

    *&+*$+#/w u

    #/w v

    ,o po,(o"&"o $/32:

  • 7/21/2019 80 exercicios CALCULO

    9/12

    R#spos(&:

    1. &2. *2. 42.

    11. 1;. 1=. 1?.

    1.

    8

    .;

    =.

    >.

    .

    B.

    1B.

    1.

  • 7/21/2019 80 exercicios CALCULO

    10/12

    8B.

    ;. ;=

    ;>. ;?.

    ;.

    ;B. ;.

    =. =1.

    =8. =;. 8/> ==. =>. =?.

    =. =B.

    =. >.

    8.

    81.

    8>

    88.

    8

  • 7/21/2019 80 exercicios CALCULO

    11/12

    >1. >8.

    >;. >=.

    >>. >?.

    >.

    >B.

    >. ?. ?1. ?8.

    ?;. ?=.

    ?>.

    ??. ?. ?B.

    ?. .

    1.

    8. / ;.

    =.

    >.

  • 7/21/2019 80 exercicios CALCULO

    12/12

    ?.

    .

    B.

    .

    B.

    B1.

    B8.

    B;.