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# test2v1 - Math 1ZA3 1st Sample Test#2 Name(Last Name(First...

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Math 1ZA3 1st Sample Test #2 Name :___________________________________________ (Last Name) (First Name) Student Number: Tutorial Number: _____________________ ____________________ This test consists of 27 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. Suppose is differentiable on . Let . Find an expression for 0 JÐBÑ œ 0Ð Ò/ ÓÑ J ÐBÑ tan " B w # (a) (b) 0 Ð Ò/ Ó † Ñ 0 Ð Ò/ ÓÑ † #B/ w " B w " B B #B/ "/ tan tan # # # B # #B # (c) (d) 0 Ð Ò/ ÓÑ † 0 Ð Ò/ ÓÑ † w " B w " B #B/ #B/ "/ "/ tan tan # # B B # # B % B # (e) 0 Ð Ò/ ÓÑ † w " B #B/ "/ tan # B # #B # 2. Find by implicit differentiation. .C .B " # sin Ð BC Ñ œ "  B C (a) (b) (c) #BC † ÐBCÑ † ÐBCÑ B † ÐBCÑ B † ÐBCÑ B #BC #BC † ÐBCÑ C "BC " # "Î# B " B " B " "BC "BC # # "BC # "Î# # "Î# # "Î# # C "BC # " "Î# (d) (e) #BC † ÐBCÑ † ÐBCÑ B † ÐBCÑ B #BC † ÐBCÑ C "BC " # "Î# B " B " "BC # "BC # "Î# # "Î# # C "BC # " "Î# 3. Let . Find . 0ÐBÑ œ B  ÐB  Ñ Ð0 Ñ Ð\$Ñ ' # " w 1 1 sin 1 1 1 1 1 1 ' # ' ' '  " 4. If and , find . 0ÐBÑ  B Ò0ÐBÑÓ œ "! 0Ð"Ñ œ # 0 Ð"Ñ # \$ w ' & "% "& "' "\$ "\$ "\$ "\$ "\$ 5. Find the numerical value of cosh ln Ð / / "& " "( # ) % ) % % % Ð sinh ln 6. Evaluate lim tanh BÄ∞ B (a) (b) (c) (d) (e) " ! ∞ " 7. Evaluate lim tanh BÄ∞ B " ! ∞ "

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