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

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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 c A a unique solution c B no solution c C in±nitely many solutions with x = 0 c D in±nitely many solutions with y = 0 c E in±nitely many solutions with z = 0 2. [3 marks] lim x 1 p 4 x x 2 1 2 x 1 P c A = 2 c B = 1 c C = 2 c D = 0 c E does not exist 1
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3. [3 marks] If f ( x ) = x x , then f (4) = c A 8 + 4 ln4 c B 4 + 4 ln4 c C 4 + 8 ln4 c D 8 + 8 ln4 c E 4 8 ln4 4. [3 marks] If y 3 + xy = 2 x 2 , then when x = 1 and y = 1 , dy dx = c A 5 4 c B 1 c C 1 2 c D 3 4 c 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 c A max = 1 , min = 5 3 c B No absolute maximum, min = 1 c C No absolute minimum, max = 3 5 c D max = 3 5 , min = 1 c E max = 1 , min = 0 2
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6. [3 marks] Let f ( x ) = x 1 3 (4 + x ) . The interval(s) on which f is decreasing is (are) c A ( −∞ , 1) and (0 , ) c B ( −∞ , 1) c C no interval c D ( −∞ , 0) c E ( 1 , 0) and (0 , ) 7. [3 marks] lim x →∞ ( 1 + 2 x ) x 3 = c A c B 1 c C e 1 / 6 c D e 2 / 3 c E e 3 / 2 8. [3 marks] i 1 0 x 3 (1 + x 4 ) 5 dx = c A 21 2 c B 21 8 c C 1 24 c D 1 4 c E 13 8 3
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9. [3 marks] The area bounded by the y -axis, the straight line y = ex and the curve y = e x is equal to c A i 1 0 ( e e x ) dx c B i e 1 ln y dy c C i e 0 ( e x ex ) dx c D i e 1 (ln y y e ) dy c E i 1 0 y e dy + i e 1 ( y e ln y ) dy 10. [3 marks] The average value of f ( x ) = x 4 over the interval [5 , 13] is c A 13 4 c B 13 6 c C 52 3 c D 1 6 c E 2 11. [3 marks] i 0 1 ( x + 2) 5 dx c A diverges c B = 0 c C = 1 16 c D = 1 16 c E = 1 64 4
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12. [3 marks] If dy dx = xy and y = 2 when x = 0 then when x = 2 , y = c A 0 c B 1 c C e 4 c D e 2 c E 2 e 2 13. [3 marks] If e x 2 = z ln y
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QuesSol2008 - FACULTY OF ARTS AND SCIENCE University of...

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