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Unformatted text preview: UNIVERSITY OF TORONTO SCARBOROUGH CAMPUS MATA26Y January 29, 1996 TERM TEST II 1. Find the indicated derivatives.  (a) x = sin t 1 + cos t . Find dx dt .  (b) y = e cos 2 . Find dy d .  (c) y = u u + 1, u = 2 x 2 + 3. Find dy du , and dy dx .  (d) p ( x ) = ln(( x- a )( x- b )( x- c )). a , b , c are constants. Find p ( x ).  (e) ( x + y ) 2 = (2 x + 1) 3 . Find dy dx . (Use implicit differentiation. Your answer will involve both x and y .) 2. According to the Globe and Mail of January 10, 1996, Statistics Canada pre- dicts that Canadas population will be 29914300 by July 1 , 1996 and 30269900 one year later. Assuming that the population growth during that time can be modelled by an exponential function, answer the following.  (a) What is the corresponding rate of growth of Canadas population per year?  (b) What is the expected doubling time?  (c) On whichdate (plus or minus a day) will Canadas population hit 30000000?...
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