QuesSol_2004

# QuesSol_2004 - FACULTY OF ARTS AND SCIENCE University of...

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Unformatted text preview: FACULTY OF ARTS AND SCIENCE University of Toronto FINAL EXAMINATIONS, APRIL/MAY 2004 MAT 133Y1Y Calculus and Linear Algebra for Commerce PART A. MULTIPLE CHOICE 1. [3 marks] If f ( x ) = ( x 2 + e 2 x ) 3 e- 2 x (1 + x- x 2 ) 2 / 3 , then f (0) = A . B . 1 C . e 10 3 D . 10 3 E . e 16 3 2. [3 marks] Let f ( x ) = e- x x ≤ ax + b x > where a and b are constants. If f is differentiable at x = 0 , then f ( x ) = 0 when x = A . 1 B . 2 C . ln 2 D . ln 3 E . e 1 3. [3 marks] The graph of y = (1- ln x ) 2 has A . no inflection points B . an inflection point at x = 1 C . an inflection point at x = 2 D . an inflection point at x = √ e E . an inflection point at x = e 2 4. [3 marks] The largest value attained by y = x ln x if 0 < x ≤ e is A . e B . 1 e C . D . 1 E . 2 5. [3 marks] lim x → 1 x 1 1- x = A . e B . 1 e C . 1 D . E . undefined 6. [3 marks] If F ( x ) = Z 7 x e t ln | t | dt , then F 00 (1) = A .- e B . e C . D .- 2 e E . 2 e 2 7. [3 marks] Z 1 x x 2 + 1 dx = A . = ln √ 2 B . diverges C . = e D . = 0 E . = ln 2- 1 8. [3 marks] The area between f ( x ) = e x 1 + e x and the x-axis from x = 0 to x = ln 5 is A . ln 3 B . 1 3 C . ln 4 D . 4 ln 5 E . 5 6 9. [3 marks] The area bounded by the graphs of y = x 2 3 and y = x 3 2 is A . 1 4 B . 1 20 C . 1 5 D . 1 10 E . 3 20 3 10. [3 marks] The determinant of A = 1 2 4 3 T 2 2 5 3- 1 1- 1 1 3 2 4 3 5 1 1 is A .- 24 B . 3 2 C . 24 D .- 5 2 E .- 3 2 11. [3 marks] To approximate Z 1 p 1 + x 3 dx dividing the interval [0 , 1] into 4 equal parts and using the Trapezoidal Rule, T 4 = A . 1 4 " 1 + r 1 + 1 64 + r 1 + 1 8 + r 1 + 27 64 # B . 1 4 " 1 + r 1 + 1 64 + r 1 + 1 8 + r 1 + 27 64 + √ 2 # C . 1 4 " 1 + r 1 + 1 64 + r 1 + 1 8 + 2 r 1 + 27 64 + √ 2 # D . 1 12 " 1 + 2 r 1 + 1 64 + 4 r 1 + 1 8 + 2 r 1 + 27 64 + √ 2 # E . 1 8 " 1 + 2 r 1 + 1 64 + 2 r 1 + 1 8 + 2 r 1 + 27 64 + √ 2 # 4 12. [3 marks] If dy dx = xy and y = 1 when x = 1 , then when x = 0 , y = A . B . 1 2 C . √ e D . 1 √ e E . 2 13. [3 marks] If f ( x, y ) = 3 x 3- 2 x 2 + 3 y- y 3 then the number of critical points of f is A ....
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QuesSol_2004 - FACULTY OF ARTS AND SCIENCE University of...

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