QuesSol_2007 - FACULTY OF ARTS AND SCIENCE University of...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
FACULTY OF ARTS AND SCIENCE University of Toronto FINAL EXAMINATIONS, APRIL/MAY 2007 MAT 133Y1Y Calculus and Linear Algebra for Commerce PART A. MULTIPLE CHOICE 1. [3 marks] The system of equations x + y + z + u + v = 1 y + z + 2 u = 2 z + u + 2 v = 3 has ± A no solutions ± B a unique solution ± C in±nitely many solutions with one parameter ± D in±nitely many solutions with two parameters ± E in±nitely many solutions with three parameters 2. [3 marks] Let h ( x ) = x 2 - 1 x - 1 for x 6 = 1 a - 2 for x = 1 Then h ( x ) is continuous everywhere for a equal to ± A 4 ± B 3 ± C 1 ± D 2 ± E - 2 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
3. [3 marks] If f ( x ) = ( x + 1) 1 x + ln x , f 0 ( x ) = ± A ( x + 1 ) 1 x + ln x h ( - 1 x 2 + 1 x ) ln ( x + 1 ) + ± 1 x + ln x ² · 1 2( x + 1) i ± B e ( 1 x + ln x ) ln ( x + 1 ) h - ( 1 x 2 + 1 x ) ln ( x + 1 ) + ± 1 x + ln x ² · 1 2 x ( x + 1) i ± C ( x + 1 ) 1 x + ln x h ( - 1 x 2 + 1 x ) ln ( x + 1 ) + ± 1 x + ln x ² · 1 ( x + 1) i ± D e ( 1 x + ln x ) ln ( x + 1 ) h ( - 1 x 2 + 1 x ) ln ( x + 1 ) 2 x + ± 1 x + ln x ² · 1 2 x ( x + 1) i ± E ( x + 1 ) 1 x + ln x h ( - 1 x 2 + 1 x ) ln ( x + 1 ) + ± 1 x + ln x ² · 1 2 x ( x + 1) i 4. [3 marks] The slope of the tangent line to the curve x 3 + 3 y 2 = 4 at (1 , 1) is ± A undeFned ± B - 1 3 ± C 4 3 ± D 3 4 ± E - 1 2 2
Background image of page 2
5. [3 marks] On the interval ( 1 2 , 2 ) , the function f ( x ) = e - ( x 2 + x - 2 ) has ± A a local minimum but no local maximum ± B a local maximum but no local minimum ± C a local maximum and a local minimum ± D neither a local maximum nor a local minimum ± E two local minima and no local maximum 6. [3 marks] lim x →∞ ( x 2 + 1) 1 x 2 +2 ± A does not exist ± B = e 1 2 ± C = e ± D = 0 ± E = 1 7. [3 marks] When using the Trapezoidal Rule with the interval [ - 2 , 6] divided into n = 4 subintervals the approximate value of Z 6 - 2 p 1 + x 2 dx is closest to ± A 23 . 04 ± B 21 . 55 ± C 22 . 19 ± D 15 . 36 ± E 14 . 37 3
Background image of page 3

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

View Full DocumentRight Arrow Icon
8. [3 marks] Z 1 - 1 x 2 3 dx (2 + x 5 3 ) 3 = ± A - 1 3 ± B 3 5 ln 27 ± C - 64 27 ± D 1 5 ± E 4 15 9. [3 marks] Z e 1 x ln x dx = ± A e 2 - e + 1 2 ± B 1 2 ± C e 2 2 ± D e 2 + 1 4 ± E 0 4
Background image of page 4
10. [3 marks] Z 3 x - 4 ( x - 1)( x - 2) dx = ± A 3 ln | ( x - 1)( x - 2) | + C ± B 3 ln ± ± ± x - 2 x - 1 ± ± ± + C ± C 3 ln ± ± ± x - 1 x - 2 ± ± ± + C ± D ln ± ± ± ( x - 1)( x - 2) 2 ± ± ± + C ± E ln ± ± ± x - 1 ( x - 2) 2 ± ± ± + C 11. [3 marks] Z 8 1 3 x dx ± A diverges ± B = 6 ± C = - 6 ± D = 4 ± E = - 4 5
Background image of page 5

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

View Full DocumentRight Arrow Icon
12. [3 marks] If f ( x, y, z ) = x 2 y 3 z 4 , f xyz (2 , - 1 , - 2) = ± A - 3 8 ± B - 3 2 ± C - 1 4 ± D 3 2 ± E 3 8 13. [3 marks] If two products called A and B have the joint demand functions q A ( p A , p B
Background image of page 6
Image of page 7
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 / 19

QuesSol_2007 - FACULTY OF ARTS AND SCIENCE University of...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online