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sample3 - Math 1ZA3 1st Sample Test#3 Name(Last Name(First...

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Math 1ZA3 1st Sample Test #3 Name :___________________________________________ (Last Name) (First Name) Student Number: Tutorial Number: _____________________ ____________________ This test consists of 16 multiple choice questions worth 1 mark each (no part marks), and 1 question worth 1 mark (no part marks) on proper computer card filling. All questions must be answered on the COMPUTER CARD with an HB PENCIL. Marks will not be deducted for wrong answers (i.e., there is no penalty for guessing). You are responsible for ensuring that your copy of the test is complete. Bring any discrepancy to the attention of the invigilator. Calculators are NOT allowed. 1. Find if , , . 0Ð"Ñ 0 Ð>Ñ œ $Î > 0Ð%Ñ œ #! 0 Ð%Ñ œ ( ww w (a) (b) (c) (d) (e) & ' ( ) * 2. Find if Ñ 0 ÐBÑ œ B B 1 $ w sec tan B 0Ð!Ñ œ # sec # , . #  # "  # $  $ #  $ $  " $ 3. Evaluate lim 8Ä∞ 3œ" 8 # $3 &3 8 8 8 $  # %& & "& %& %& % # 4. If you were to use use Mathematical Induction to show that , which of the 3œ" 8 # 8Ð8"ÑÐ#8"Ñ ' 3 œ following would be the second step? 5 5 # # 5Ð5"ÑÐ#5"Ñ Ð5"ÑÐ5#ÑÐ#5$Ñ ' ' 3 œ Ð3  "Ñ œ , and show that 5 5" # # 5Ð5"ÑÐ#5"Ñ Ð5"Ñ5Ð#5"Ñ ' ' 3 œ 3 œ , and show that 5 5" # # 5Ð5"ÑÐ#5"Ñ Ð5"Ñ5Ð#5"Ñ ' ' 3 œ 3 œ , and show that 5 5" # # 5Ð5"ÑÐ#5"Ñ Ð5"ÑÐ5#ÑÐ#5$Ñ ' ' 3 œ 3 œ , and show that 5 5" # # 5Ð5"ÑÐ#5"Ñ Ð5"ÑÐ5#ÑÐ#5$Ñ ' ' 3 œ 3 œ , and show that 5. Write the following sum in sigma notation: . $ & ( "( % * "' )"  â  (a) (b) (c) (d) (e) 3œ" 3œ" 3œ! 3œ" 3œ" ( ) ) ) 8 Ð#3"Ñ Ð#3"Ñ Ð#3"Ñ Ð#3"Ñ Ð3"Ñ Ð3"Ñ Ð3"Ñ Ð3"Ñ Ð3"Ñ #3 # # # # #
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