# 1995final - SCARBOROUGH CAMPUS UNIVERSITY OF TORONTO...

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Unformatted text preview: SCARBOROUGH CAMPUS UNIVERSITY OF TORONTO MATA26Y April 23, 1996 FINAL EXAMINATION 1. Find the following antiderivatives: (Remember that you can check your answer!) [4] (a) Z 4 + x x dx [4] (b) Z 1 + sin(2 x ) 2 dx [4] (c) Z 1 (1 + x ) 2 dx [4] (d) Z ln | 1 + x | 1 + x dx [4] (e) Z log 3 1 x dx 2. Find the derivatives of the following functions: [2] (a) f ( x ) = x 2 ln( x 2 ) [2] (b) g ( x ) = x 2 + 4 x 2- 4 [2] (c) h ( x ) = ( x 2 + 1)arctan x [2] (d) m ( x ) = sin(cos( e 3 x )) [2] (e) n ( x ) = arcsin 2 x [10] 3. Let S ( t ) be the number of daylight hours, in Cambridge, MA, at the t th day of the year. During spring (from the vernal equinox, t = 80, to the summer solstice, t = 173), the graph of S ( t ) is concave down and of course in- creasing. In the table to the right we list some values of S ( t ). What is the average length of the days in spring (in hours and minutes)?...
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## This note was uploaded on 10/04/2011 for the course MATH 16121 taught by Professor Rachelbelinsky during the Spring '11 term at Georgia State University, Atlanta.

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1995final - SCARBOROUGH CAMPUS UNIVERSITY OF TORONTO...

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