QuesSol_2001

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

This preview shows pages 1–6. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 15

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online