QuesSol_2003

# QuesSol_2003 - 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 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 first 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

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

View Full Document
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
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

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

View Full Document
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
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.

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.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern