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# sampleexam - Math 1Z04 Sample Final Exam Name(Last...

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Math 1Z04 Sample Final Exam Name :___________________________________________ (Last Name) (First Name) Student Number: Tutorial Number: _____________________ ____________________ This exam consists of 59 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. Sketch the graph of 0ÐBÑ œ B\$B "Î\$ (a) (b) (c) (d) (e)

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2. Find the shortest distance from the parabola to the point . C œ B  # Ð%ß \$Ñ " # # (a) (b) (c) (d) (e) È È È #" & \$# 3. Find the equation of the tangent line to the curve at the point . C œ Ð BÑÎB Ð/ß "Î/Ñ ln (a) (b (c (d (e) ) ) ) Cœ B" CœB Cœ B Cœ/B "" " // / 4. The graph of a function is shown. Which graph is an antiderivative of ? 00 (a) 0ÐBÑ (b) (c) (d) (e)
5. Evaluate the following limit, lim sinh BÄ_ B B / (a) (b) (c) (d) (e) #! _ " " # 6. Find the critical numbers of the function . 0ÐBÑ œ B ÐB%Ñ %Î& # (a) (b) (c) (d (e ) ) %ß !ß " "ß % %ß !ß % %ß ! ) ( 7. Suppose that the derivative of the function is given by 0ÐBÑ 0ÐBÑœ %B ' B Ñ w "Î\$ #Î\$ . Find the interval(s) on which is increasing. 0 (a) (b) (c) (d) (e) Ð_ß %Ñß Ð'ß _Ñ Ð_ß %Ñ Ð_ß !Ñß Ð%ß 'Ñ Ð!ß %Ñ Ð!ß %Ñß Ð'ß _Ñ 8. Find the horizontal asymptotes (if any) of the function given by 0ÐBÑ œ / "/ B B . (a) (b) (d) ( none (c) " # ß" " ! e) !ß " 9. Evaluate the following limit lim sin cos 1 B " B (a) (b) (c) (d) (e) ! __ " " # 10. Evaluate the following limit lim tan BÄ_ B Ð"ÎBÑ (a) (b) (c) (d) (e) d.n.e. "!_ 11. Find all points in the interval at which the tangent line to is Ò!ß # Ó 0ÐBÑ œ # B  B 1 cos cos # horizontal. (a) (b) (c) (d) (e) !ß ß # !ß ß ß ß # ß 11 1 1 1 1 ## # # \$

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12. Evaluate the following limit lim 8Ä_ 3œ" 8 \$ " –— Œ "3 88 " (a) (b) (c) (d) (e) \$(& \$ #%% % " 13. Evaluate the following telescoping sum " 3œ" "!! 33 " Ð&  & Ñ (a) (b) (c) (d) (e) & && & " "& "!! "!! ** "!! ** 14. Find if C w B C BÎC (a) (b) (c) (d) (e) C Ð / C Ñ C C Ð C " Ñ C C Ð C Ñ B/ C B / # BÎC BÎC BÎC BÎC BÎC BÎC # BÎC # BÎC BÎC BÎC # 15. Evaluate the following limit, lim 2Ä! \$ Ð#  2Ñ  ) 2 (a) (b) (c) (d) (e) )" #" !*" " 16. Evaluate the following limit, lim BÄ" # B# ÐB  "Ñ (a) (b) c) (d) (e) ( d.n.e. _ _ " ! 17. Let 0ÐBÑ œ / "#/ B B Find a formula for . B Ñ " (a) (b) (c) (d) (e) ln ln ln ln ln ˆ‰ ˆ ˆ B# B # B B B #B "B "B "#B "#B 18. Find all points on the graph of at which the tangent line is horizontal.
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sampleexam - Math 1Z04 Sample Final Exam Name(Last...

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