Test 2 MA211 2016paper2.pdf - University of the South...

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University of the South Pacific School of Computing, Information and Mathematical Sciences MATH211 Advanced Calculus Semester 1, 2016 SHORT TEST 2 Duration 50 minutes INSTRUCTIONS: 1. All questions are compulsory. Show all your working. Start each question on a new page. 2. Marks for each question are as indicates. The total is 30. 3. You may use a scientific or graphical calculator. Question1 (4+4+(3+5)=16 marks) (a) Evaluate the triple integral integraldisplayintegraldisplayintegraldisplay G 12 xy 2 z 3 dV over the rectangular box G defined by the inequalities 1 x 2, 0 y 3, 0 z 2. (b) Find the divergence and the curl of the vector field F ( x , y , z )= xz 3 i + 2 y 4 x 2 j + 5 z 2 y k . (c) Consider the vector field F = parenleftbigg 6 x 2 2 xy 2 + y 2 x parenrightbigg i parenleftBig 2 x 2 y 4 x parenrightBig j

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