QuesSol_2003 - FACULTY OF ARTS AND SCIENCE University of...

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FACULTY OF ARTS AND SCIENCE University of Toronto FINAL EXAMINATIONS, APRIL/MAY 2003 MAT 133Y1Y Calculus and Linear Algebra for Commerce PART A. MULTIPLE CHOICE 1. [3 marks] A $100,000 mortgage is to be repaid over 10 years by equal monthly payments made at the end of each month; that is, the ±rst payment is one month after the loan is made. If interest is 10% compounded semiannually, the amount of each payment is ± A $1,264.45 ± B $1,310.34 ± C $1,273.96 ± D $1,299.72 ± E $1,335.10 2. [3 marks] A $100 bond with 10 years until maturity has semiannual coupons at an annual coupon rate of 10%. If its annual yield is 9%, then its market price is ± A $108.48 ± B $107.76 ± C $105.97 ± D $109.03 ± E $106.50 3. [3 marks] If A is a 4 × 4 matrix and det( A ) = 5 , then det(3 A 2 ) = ± A 225 ± B 75 ± C 2025 ± D - 75 ± E 300 1
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4. [3 marks] f ( x ) = ( x 2 - 4) 1 / 3 has ± A an absolute minimum at x = 0 and no absolute maximum ± B absolute minimums at x = 2 and x = - 2 and a relative maximum at x = 0 ± C a relative minimum at x = 0 and absolute maximums at x = - 2 and x = 2 ± D a relative maximum at x = 0 and no relative minimums ± E no relative maximums or minimums 5. [3 marks] If the cost function is given by: c = 0 . 01 q 2 + 6 q + 100 Then average cost ¯ c is minimized when q = ± A 300 ± B 0 ± C 1 ± D 100 ± E 1000 6. [3 marks] lim x + ln(1 + e 2 x ) x ± A is 1 ± B is 4 ± C is 0 ± D is 2 ± E does not exist 2
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7. [3 marks] Z e 4 e 1 x (ln x ) 1 2 dx = ± A 1 e 2 ± B 1 2 e 4 ± C 1 2 e 4 - 1 2 e ± D 2( e - e ) ± E 2 8. [3 marks] If Z x 1 f ( t ) dt = e x ln x when x > 0 , then f (1) = ± A e ± B 2 ± C 1 ± D 0 ± E e x ln x 9. [3 marks] Z x 2 + 1 x 2 + x dx = ± A x + ln | x |- 2 ln | x + 1 | + C ± B ln | x | + ln | x + 1 | + C ± C x - 1 + 2( x + 1) - 1 + C ± D x - ln x + 2 ln( x + 1) + C ± E ln ± ± ± x x + 1 ± ± ± + C 3
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10. [3 marks] Using a subdivision of the interval [1 , 3] into 4 subintervals of equal length, the trapezoidal rule yields the following approximation for Z 3 1 1 ln( x + 1) dx : ± A 1 . 8722 ± B 2 . 7230 ± C 1 . 7342 ± D 0 . 9863 ± E 1 . 9409 11. [3 marks] If a > 0 , Z 0 axe - ax dx ± A diverges ± B equals a ± C equals 1 a ± D equals 1 ± E equals e - a 12. [3 marks] If dy dx = 2 xy and y = e when x = 0 then, when x = 1 , y = ± A 1 ± B e ± C e 2 ± D e 3 ± E e 4 4
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13. [3 marks] If f ( x, y ) = e xy , then when x = 2 and y = 3 , 3 f ∂x∂y 2 = ± A 24 e 6 ± B 16 e 6 ± C 30 e 6 ± D 12 e 6 ± E 18 e 6 14. [3 marks] Let x ( r, s
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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_2003 - FACULTY OF ARTS AND SCIENCE University of...

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