Practice Midterm I - 3

Practice Midterm I - 3 - Math 1N03 1=> Sample Test #2...

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Math 1N03 1 Sample Test #2 => Name :___________________________________________ (Last Name) (First Name) Student Number: Tutorial Number: _____________________ ____________________ This test has two parts. The first part consists of 10 multiple choice questions, and the second part consists of 3 long answer questions. You are responsible for ensuring that your copy of the test is complete. Bring any discrepancy to the attention of the invigilator. Part I Instructions for Part I : Part I consists of 10 multiple choice questions worth 1 mark each (no part marks) and 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). 1. The following limit represents the derivative of some function at some number . 0+ State such an and . lim 2Ä! Ð"2Ñ 2 ln (a) (b) , 0ÐBÑ œ Ð"  BÑß + œ ! 0ÐBÑ œ B + œ " ln ln (c) (d) 0ÐBÑœ# B ß+œ" 0ÐBÑœ" Ð"BÑ ß+œ! ln ln (e) all of the above 2. Suppose that and . Find 0Ð&Ñ œ "ß 0 Ð&Ñ œ #ß 1Ð&Ñ œ &ß 1 Ð&Ñ œ $ ww Ò1ÎÐ0  1ÑÓ Ð&Ñ #w (a) (b) (c) (d) (e) "' "& "( "( "& $' $' ' $' ' 3. If and , find 2Ð%Ñ œ $ 2 Ð%Ñ œ ( B 2ÐBÑ w# . .B Bœ% k ab (a) (b) (c) (d) (e) )) &$ '' (( )# 4. (a) (b) If and are the functions whose graphs are shown, let . Find , if it exists. 01 @ÐBÑ œ 1Ð0ÐBÑÑ @ Ð"Ñ w ' '#! d.n.e. (c) (d) (e) 5. Suppose is differentiable on . Let . Find an expression for 0 JÐBÑ œ 0Ð Ò/ ÓÑ tan " B # JÐBÑ 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 #
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6. Find lim tan BÄ_ " %B $B 'B B Š‹ # $ (a) (b) (c) (d) (e) !_ Ð Ñ 11 #$ # " # tan 7. (a) (b) (c) Match the graph of the function below with the graph of its derivative in I-IV. I II II I IV none of them (d) (e) 8. Find an equation of the tangent line to the curve at the point B# B sec cos Ð Î$ß "Ñ 1 . (a) (b) Cœ# $BÐ"# $ Ñ BÐ" $ Ñ ÈÈ È È $ # (c) (d) Cœ BÐ" Î#Ñ Cœ$ $BÐ" " # (e) C œ $B  Ð"  "Î $ Ñ 1 9. (a) (b) (c) (d) (e) 10. Use the given graph to the right to estimate the value of Fo 0Ð%Ñ w " $# " % r what values of does the function satisfy the equation ?
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This note was uploaded on 11/25/2009 for the course MATH MATH 1A03 taught by Professor Dr.lozinski during the Fall '09 term at McMaster University.

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Practice Midterm I - 3 - Math 1N03 1=> Sample Test #2...

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