1007Test1_09sol - Test 1 Wednesday MATH 1007G Last Name ID...

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Test 1, Wednesday January 28, 2009 MATH 1007G Last Name :_________________ First Name:_______________ ID #:____________________ Total marks:36 Total time: 50 minutes No Calculators are allowed. Show your work. Question 1. [3 marks] Find an expression for the function f whose graph is the straight line through the points ( , ) 3 5 and ( , ) 2 4 - in the xy - plane. The slope of the straight line through the points ( , ) 3 5 and ( , ) 2 4 - is m = - - - = 5 4 3 2 9 ( ) The equation of the straight line is y x y x - = - = - 5 9 3 9 22 ( ) So f x x ( ) = - 9 22 is the function. Question 2. a) [3 marks] Find all the values of x in [ ] 0 2 , π such that 2 2 0 sin sin cos x x x = . 2 2 0 2 1 0 sin sin .cos sin ( cos ) x x x x x = = So, either sin x = 0 or 1 0 = cos x Since x in [ ] 0 2 , π , sin , , x x = = 0 0 2 π π and 1 0 = = cos x x π So, x = 0 2 , , π π Question 3. [10 marks] Simplify a) log log log log * log log 2 15 2 6 2 20 2 15 6 20 2 1 8 2 2 3 3 - - = = = - = - b) log (ln ) ( )ln log ( ) ln( ) ( ) / 5 5 1/2 5 5 2 1/2 0 2 2 1 2 e e x x e x x x x x x - = - = - = - = c) 3 12 4 3 2 x y x x y + where x < 0 while y 0 . 3 12 4 3 2 32 3 2 3 x y x x y x y x x y + = + - . . . ( ) = - = - = 6 3 2 3 2 3 2 6 1 5 3 2 . ( ) x y x y x y x y d) ( ) / ( ) ( ) 27 6 4 3 27 6 3 4 3 2 4 1 81 8 1 81 8 x x x x x - = - = - = = - e) cos(tan ) - 1 x
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