# sample2 - Math 1Z04 1st Sample Test #2 Name:_ (Last Name)...

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Math 1Z04 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 " B B #B/ "/ tan tan ## # B # #B # (c) (d) 0 Ð Ò/ ÓÑ † 0 Ð Ò/ ÓÑ † " B " B #B/ #B/ "/ "/ tan tan BB B % B # (e) 0 Ð Ò/ ÓÑ † " B #B/ "/ tan # B # #B # 2. Find by implicit differentiation. .C .B " # sin ÐB C Ñœ " B C È (a) (b) (c) #BC † ÐBCÑ †Ð B C Ñ B B C Ñ B B C Ñ B #BC #BC † ÐBCÑ C "BC " # "Î# B" B " "BC "BC # # "BC # "Î# # "Î# # "Î# # C "BC # " "Î# È ÈÈ (d) (e) #BC † ÐBCÑ B C Ñ B B C Ñ B #BC † ÐBCÑ C "BC " # "Î# B " "BC #" B C # "Î# # "Î# # C "BC # " "Î# È È 3. Let . Find . 0ÐBÑ œ B ÐB Ñ Ð0 ÑÐ\$Ñ ' # " w 1 1 sin (a) (b) (c) (d) (e) 11 1 1 ' # ' '' " 4. If and , find . 0ÐBÑ  B Ò0ÐBÑÓ œ "! 0Ð"Ñ œ # 0 Ð"Ñ #\$ w (a) (b) (c) (d) (e)  ' & "% "& "' "\$ "\$ "\$ "\$ "\$ 5. Find the numerical value of cosh ln Ð% Ñ (a) (b) (c) (d) (e) // "& " "( #) % ) % % % Ñ sinh ln 6. Evaluate lim tanh BÄ_ B (a) (b) (c) (d) (e) "!_ _ " 7. Evaluate lim tanh BÄ_ B (a) (b) (c) (d) (e) "

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8. If , find . 0ÐBÑ œ Ð 0 / ln ln w# ab (a) (b) (c) (d) (e) "" #"% #/ # / # / ## ln 9. Find the horizontal asymptotes of 0ÐBÑ œ / /B B B (a) (b) (c) (d) (e) none Cœ" Cœ! Cœ" ß! ß" 10. Find the value of the limit . lim BÄ" Ð#BÑ B ln ln (a) (b) (c) (d) (e) " # "# __ 11. Let . Find the intervals (if any) where is concave up. 0ÐBÑœ B  B B# 0 %\$ (a) (b) (c) Ð_ß !Ñ Ð ß _Ñ Ð ß _Ñß Ð ß _Ñ # \$\$ \$ (d) (e) Ð_ß!ÑßÐ ß_Ñ Ð_ß ÑßÐ!ß_Ñ 12. The function is: 0ÐBÑ œ B " B (a) (b) Increasing on Decreasing on Ð"ß !Ñ Ð!ß "Ñ (c) (d) Increasing on Decreasing on Ð!ß "Ñ Ð"ß _Ñ (e) Increasing on Ð!ß _Ñ 13. Find if CC œ ÐB Ñ wB cos ln (a) (b) ln cos sin cos ln cos Ð Ð Ð BÑ † Ñ " B " B ln ln (c) (d) Ð Ð BÑ  B B Ð B  B B cos ln cos tan ln cos cos sin ln ln ln BB ˆ‰ ˆ (e) " B ln cos tan ln Ñ B B " 14. Consider the function given in the graph below.
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## This note was uploaded on 02/05/2010 for the course MATH 1Z04 taught by Professor Childs during the Spring '08 term at McMaster University.

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sample2 - Math 1Z04 1st Sample Test #2 Name:_ (Last Name)...

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