Mathematics Test Three

# Mathematics Test Three - Math 1ZA3 1st Sample Test for...

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Math 1ZA3 1st Sample Test for Suggested Problems #4 Name :___________________________________________ (Last Name) (First Name) Student Number: Tutorial Number: _____________________ ____________________ This test consists of 18 multiple choice questions worth 1 mark each (no part marks). 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 the Taylor series for 0ÐBÑ œ " B \$ centered at . +œ# (a) " # 8œ" 88 "†%†(†â†Ð\$8#Ñ '8 x \$ 8  "  Ð"Ñ ÐB  #Ñ (b) " # 8œ" #†&†)†â†Ð\$8"Ñ x \$ 8 "  Ð"Ñ ÐB  #Ñ (c) " # 8œ" "†%†(†â†Ð\$8#Ñ x \$ 8" "  Ð"Ñ ÐB  #Ñ (d) " # 8œ" #†&†)†â†Ð\$8"Ñ ' \$ 8 "  Ð"Ñ ÐB  #Ñ (e) " # 8œ" #†&†)†â†Ð\$8"Ñ x \$ 8" "  Ð"Ñ ÐB  #Ñ 2. Find the sum of the series " /  â /// #x \$x %x #\$% (a) (b) (c) (d) (e) // " Ð / ÑÐ / Ñ / / cos sin 3. Use series to evaluate the following limit lim sin BÄ! "! * #) B B Ð B Ñ B (a) (b) (c) (d) (e) """"" #\$'*# )

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4. Consider the Taylor polynomial for at . Use Taylor's inequality to X ÐBÑ 0ÐBÑ œ B + œ " \$ \$Î% estimate the accuracy of the approximation when lies in the interval 0ÐBÑ ¸ X ÐBÑ B \$ !Þ) Ÿ B Ÿ "Þ# . (a) (b) (c) (d) "\$& & "\$& & "\$& & "& & %x #! % %x #! ' %x "! % \$x#! % "\$Î% "\$Î% "\$Î% *Î% %%%\$  (e) "& & \$x#! ' *Î% \$ 5. v Consider the point and the vector . Find a point such that has TÐ"ß#ß#Ñ œØ"ß\$ß"Ù U TU Ä the opposite direction to . v (a) (b) (c) (d) (e) Ð"ß #ß "Ñ Ð"ß )ß %Ñ Ð#ß "ß "Ñ Ð!ß &ß \$Ñ Ð%ß (ß "Ñ 6. Find the parametric equations of the line passing through the points and TÐ\$ß "ß %Ñ UÐ\$ß "ß &Ñ . (a) (b) (c) (d) (e) Bœ\$> Bœ\$ Bœ\$> Bœ> Bœ! Cœ> Cœ" Cœ"> Cœ> Cœ! Dœ"%> Dœ%> Dœ> 7. Find the point of intersection (if any) of the following pairs of lines. Bœ%#= Cœ"#> Cœ'\$= Dœ\$\$> Dœ"= (a) (b) (c) (d) (e) none Ð"ß "ß #Ñ Ð"ß #ß %Ñ Ð"ß "ß !Ñ Ð#ß \$ß !Ñ 8. Find the equation of the plane passing through , and . EÐ#ß "ß \$Ñß FÐ\$ß "ß &Ñ GÐ"ß #ß \$Ñ (a) (b) %B  #D  # œ ! "!B  %C  D  #" œ ! (c) (d) 'B  \$D  \$ œ ! )B  C  \$D  ) œ !
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## This note was uploaded on 12/12/2011 for the course CHEM 1E03 taught by Professor Barbier during the Winter '08 term at McMaster University.

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Mathematics Test Three - Math 1ZA3 1st Sample Test for...

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