final-05 - Faculty of Arts and Science University of...

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Unformatted text preview: Faculty of Arts and Science University of Toronto MAT 137Y1Y Calculus! April/May Examinations; May 4, 2005 Time Alloted: 3 hours Examiners: P. Blue, M. Branker, D. Cheliotis, N. Derzko, G. Karali, A. Igelfeld, F. Latremoliere, S. Uppal 1. Evaluate the following expressions; simplify your answer whenever possible. (4%) (i) lim x → 1 ln x x 4- 1 . (4%) (ii) d dx Z x 3 dt √ 1 + t 4 ! . (5%) (iii) Z 1 e x 4- e x dx . (5%) (iv) Z dx ( x- 1 )( x- 2 ) . (6%) (v) Z √ 9- x 2 x 2 dx . 2. (7%) (i) State the precise definition of the statement lim x → a f ( x ) = L and use the definition to show that lim x → 5 x 2 = 25. (5%) (ii) Determine the points for which the function f ( x ) = x 3- 1 x- 1 , x < 1 , 2 / x 3 , 1 ≤ x < 2 , 1 4- 1 x 2 x- 2 , x ≥ 2 . is discontinuous. Justify your answer. (10%) 3. A box with a square base and an open top must have a surface area of 48 m 2 . What are the dimensions of the box that maximizes volume? Make sure that the dimensions you obtaindimensions of the box that maximizes volume?...
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This note was uploaded on 10/14/2010 for the course MAT MAT taught by Professor Unknown during the Spring '10 term at Touro CA.

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final-05 - Faculty of Arts and Science University of...

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