QuesSol2008 - FACULTY OF ARTS AND SCIENCE University of...

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Unformatted text preview: FACULTY OF ARTS AND SCIENCE University of Toronto FINAL EXAMINATIONS, APRIL/MAY 2008 MAT 133Y1Y Calculus and Linear Algebra for Commerce PART A. MULTIPLE CHOICE 1. [3 marks] The system x 2 y z = 1 x + 2 y + 5 z = 1 2 x 4 y 6 z = 2 has circlecopyrt A a unique solution circlecopyrt B no solution circlecopyrt C infinitely many solutions with x = 0 circlecopyrt D infinitely many solutions with y = 0 circlecopyrt E infinitely many solutions with z = 0 2. [3 marks] lim x 1 parenleftBig 4 x x 2 1 2 x 1 parenrightBig circlecopyrt A = 2 circlecopyrt B = 1 circlecopyrt C = 2 circlecopyrt D = circlecopyrt E does not exist 1 3. [3 marks] If f ( x ) = x x , then f (4) = circlecopyrt A 8 + 4 ln4 circlecopyrt B 4 + 4 ln4 circlecopyrt C 4 + 8 ln4 circlecopyrt D 8 + 8 ln4 circlecopyrt E 4 8 ln4 4. [3 marks] If y 3 + xy = 2 x 2 , then when x = 1 and y = 1 , dy dx = circlecopyrt A 5 4 circlecopyrt B 1 circlecopyrt C 1 2 circlecopyrt D 3 4 circlecopyrt E 1 4 5. [3 marks] The (absolute) maximum value and (absolute) minimum value of f ( x ) = x 2 4 x 2 + 4 on [ 4 , 4] are circlecopyrt A max = 1 , min = 5 3 circlecopyrt B No absolute maximum, min = 1 circlecopyrt C No absolute minimum, max = 3 5 circlecopyrt D max = 3 5 , min = 1 circlecopyrt E max = 1 , min = 0 2 6. [3 marks] Let f ( x ) = x 1 3 (4 + x ) . The interval(s) on which f is decreasing is (are) circlecopyrt A ( , 1) and (0 , ) circlecopyrt B ( , 1) circlecopyrt C no interval circlecopyrt D ( , 0) circlecopyrt E ( 1 , 0) and (0 , ) 7. [3 marks] lim x ( 1 + 2 x ) x 3 = circlecopyrt A circlecopyrt B 1 circlecopyrt C e 1 / 6 circlecopyrt D e 2 / 3 circlecopyrt E e 3 / 2 8. [3 marks] integraldisplay 1 x 3 (1 + x 4 ) 5 dx = circlecopyrt A 21 2 circlecopyrt B 21 8 circlecopyrt C 1 24 circlecopyrt D 1 4 circlecopyrt E 13 8 3 9. [3 marks] The area bounded by the y-axis, the straight line y = ex and the curve y = e x is equal to circlecopyrt A integraldisplay 1 ( e e x ) dx circlecopyrt B integraldisplay e 1 ln y dy circlecopyrt C integraldisplay e ( e x ex ) dx circlecopyrt D integraldisplay e 1 (ln y y e ) dy circlecopyrt E integraldisplay 1 y e dy + integraldisplay e 1 ( y e ln y ) dy 10. [3 marks] The average value of f ( x ) = x 4 over the interval [5...
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QuesSol2008 - FACULTY OF ARTS AND SCIENCE University of...

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