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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!)  (a) Z 4 + x x dx  (b) Z 1 + sin(2 x ) 2 dx  (c) Z 1 (1 + x ) 2 dx  (d) Z ln | 1 + x | 1 + x dx  (e) Z log 3 1 x dx 2. Find the derivatives of the following functions:  (a) f ( x ) = x 2 ln( x 2 )  (b) g ( x ) = x 2 + 4 x 2- 4  (c) h ( x ) = ( x 2 + 1)arctan x  (d) m ( x ) = sin(cos( e 3 x ))  (e) n ( x ) = arcsin 2 x  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.
- Spring '11