Practice Final

Practice Final - Math E-21a Practice Final Exam Fall 2009...

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Math E-21a Practice Final Exam– Fall 2009 The following problems appeared on previous Final Exams. Neither the number of problems nor the type of problems are necessarily indicative of problems that will appear on this semester’s exam, but they should provide good preparation for the exam. Exam topics will range over the entire course with additional emphasis on topics covered after the last midterm exam. 1 ) True or False (circle one – you need not show your work): a) The dot product of two nonzero vectors gives the cosine of the angle between these two vectors. T F b) () ( )   uvw uwv for all vectors u , v , w . T F c) The line integral of the vector field (, ) ( ,) x yy x   F along the counterclockwise boundary of any region R in the xy -plane is twice the area of R . T F d) If F is a vector field in R 3 , then (2 ) 8 ( ) curl curl FF . T F e) If F is a vector field that is everywhere tangent to a surface S , then the flux S d  FS of F through S is zero.
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