QuesSol_2001 - FACULTY OF ARTS AND SCIENCE University of...

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FACULTY OF ARTS AND SCIENCE University of Toronto FINAL EXAMINATIONS, APRIL/MAY 2001 MAT 133Y1Y Calculus and Linear Algebra for Commerce PART A. MULTIPLE CHOICE 1. [3 marks] If Mr. Smith borrows $5000 from Ms. Jones and repays the loan 125 days later by giving her $5100, what is the e±ective annual interest rate of the loan, to the nearest 0.01%? (Note: 1 year = 365 days) ± A 2.00% ± B 6.13% ± C 4.88% ± D 5.95% ± E 5.84% 2. [3 marks] Let A = 1 0 1 0 1 0 - 1 1 0 . If X = A - A - 1 , then the entry in the ²rst row and the second column of X is ± A 2 ± B - 3 ± C 3 ± D - 1 ± E 0 1
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3. [3 marks] For how many values of k does the system x + 2 y - 3 z = 4 3 x - y + 5 z = 2 4 x + y + ( k 2 - 14) z = k + 2 have no solution? ± A for no values of k ± B for two values of k ± C for one value of k ± D for three values of k ± E for in±nitely many values of k 4. [3 marks] Given f ( x ) = 2 1 x +1 + a if x < - 1 x 2 - 1 x - 1 if - 1 x < 1 b - x if x 1 If f is continuous at x = ² 1 , then ± A a = - 1 and b = - 1 ± B a = 0 and b = 3 ± C a = 0 and b = 1 ± D a = 2 and b = 3 ± E a = 0 and b = 2 5. [3 marks] lim x 0 ln(1 - x ) e x - 1 ± A does not exist ± B equals zero ± C equals 1 ± D equals - 1 ± E equals 2 2
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6. [3 marks] The average value of f ( x ) = x 9 on the interval [0 , 10] is ± A 8 9 ± B 10 9 ± C 5 9 ± D 9 8 ± E 10 8 7. [3 marks] Z 2 x ln( x + 1) dx = ± A 2 x ± ( x + 1) ln( x + 1) - ( x + 1) ² + C ± B x 2 ln( x + 1) - 2 x 3 3( x + 1) 2 + C ± C 2 x x + 1 - 2 ln( x + 1) + C ± D x 2 ln( x + 1) - x 3 3 ln( x + 1) + C ± E ( x 2 - 1) ln( x + 1) - x 2 2 + x + C 8. [3 marks] The dollar value 20 years from now of a continuous annuity with payment at time t at the rate of $500/yr and interest at 5% compounded continuously is ± A 10000(1 - e ) ± B 10000 ³ 1 - 1 e ´ ± C 25( e - 1) ± D 500( e - 1) ± E 10000( e - 1) 3
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9. [3 marks] Z 2 1 x 5 dx ± A diverges ± B equals 1 64 ± C equals 16 3 ± D equals 1 384 ± E equals - 16 3 10. [3 marks] Approximating Z 4 1 ln x dx by using the Trapezoidal Rule with n = 3 , the answer is closest to ± A 3 . 058 ± B 1 . 881 ± C 2 . 469 ± D 2 . 393 ± E 1 . 494 11. [3 marks] Suppose f ( x ) is a continuous function for all x , and that Z 9 4 f ( x ) dx = 7 , then Z 3 2 xf ( x 2 ) dx = ± A 7 2 ± B 45 7 ± C 49 10 ± D 7 ± E 9 4
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12. [3 marks] If dy dx = xy , and y = 5 when x = 0 , then when x = 1 , y is closest to ± A 8 . 24 ± B 5 . 65 ± C 5 . 10 ± D 3 . 03 ± E 1 13. [3 marks] If u ( x, y ) = e x y , x = 2
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This note was uploaded on 03/25/2010 for the course MATH MAT133 taught by Professor / during the Spring '09 term at University of Toronto.

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QuesSol_2001 - FACULTY OF ARTS AND SCIENCE University of...

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