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1995test2

# 1995test2 - UNIVERSITY OF TORONTO SCARBOROUGH CAMPUS...

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UNIVERSITY OF TORONTO SCARBOROUGH CAMPUS MATA26Y January 29, 1996 TERM TEST II 1. Find the indicated derivatives. [4] (a) x = sin t 1 + cos t . Find dx dt . [4] (b) y = e cos 2 θ . Find dy . [4] (c) y = u u + 1, u = 2 x 2 + 3. Find dy du , and dy dx . [4] (d) p ( x ) = ln(( x - a )( x - b )( x - c )). a , b , c are constants. Find p ( x ). [4] (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 Canada’s 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. [2] (a) What is the corresponding rate of growth of Canada’s population per year? [3] (b) What is the expected doubling time? [5] (c) On whichdate (plus or minus a day) will Canada’s population hit 30000000? [4] 3. (a) State the First Derivative Test for Local Maxima and Minima. [6] (b) Let f be a function. Is the following sentence true or false?

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1995test2 - UNIVERSITY OF TORONTO SCARBOROUGH CAMPUS...

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