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M408D Exam 3.pdf

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School
University of Texas at Austin
Department
Mathematics
Course
M 408C
Professor
Gary, Berg
Semester
Fall

Description
M408D   Exam  3   Summer  ‘09     Name________________________________                  EID_____________   TA________________     Each  numbered  problem  is  worth  10  points.  Show  your  work.     1)   Find  a  vector  equation  and  parametric  equations  for  the  line  segment  that   joins   P(1,0,1)  to Q(2,3,1) .       €   €                               2)   Find  the  unit  tangent  vector   T(t)  at  the  point  on  the  curve  parameterized  by   2 r(t) = 4 t i+ t j+ tk  at  the  point  given  by   t =1 .         € € €         1   M408D   Exam  3   Summer  ‘09     Name________________________________                  EID_____________   TA________________     Each  numbered  problem  is  worth  10  points.  Show  your  work.     2 3)   Find  and  sketch  the  domain  of   f (x,y) = 1+ x − y .  (7pts)   What  is  the  range  of  f?  (3pts)       €                                 2 2 4)   Show  that   lim x − y  does  not  exist.   (x,y)→(0,0) x + y 2         €       2   M408D   Exam  3   Summer  ‘09     Name________________________________                  EID_____________   TA________________     Each  numbered  problem  is  worth  10  points.  Show  your  work.     5)   Find  all  the  second  partial  derivatives  of   f (x,y) = x y +2x y 3 5 4 .           €                             6)   Find  the  equation  to  the  tangent  plane  to  the  surface  given
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