# sample1 - Math 1ZB3 1st Sample Test #1 Name:_ (Last Name)...

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Math 1ZB3 1st Sample Test #1 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. Use the definition of area to find an expression for the area under the graph of as a limit. 0 Do not evaluate the limit. , 0ÐBÑœ B / \$ \$ŸBŸ) sin B (a) lim sin 8Ä∞ 3œ" 8 &3 & 88  ÐÑ / \$ &3 8 (b) lim sin 8Ä∞ 3œ" 8 )3 ) Ð" Ñ Ð"  Ñ /  \$ )3 8 (c) lim sin 8Ä∞ 3œ" 8 &3 & Ð\$ Ñ Ð\$  Ñ /  \$ &3 8 (d) lim sin 8Ä∞ 3œ" 8 )3 ) \$ )3 8 (e) lim sin 8Ä∞ 3œ" 8 &3 & Ð" Ñ Ð"  Ñ /  \$ &3 8 2. Write as a single integral in the form : + , 0ÐBÑ.B  ! # % ##  # 0ÐBÑ.B  0ÐBÑ.B  (a) (b) (c) (d)  % % % % # # #! (e) % # 3. Estimate the area under the graph of from to using three 0ÐBÑœ%B Bœ" Bœ# # rectangles and left endpoints. (a) (b) (c) (d) (e) "! ( * \$( "( %# 4. If , find the value of . JÐBÑœ / .> J "  BB " > w # # (a) (b) (c) (d) (e)  \$\$ \$ " " // / / / %%

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5. (a) (b) (c) Let be the function whose graph is given to the right. Evaluate 0ÐBÑ 0ÐBÑ.B \$ * ) ) "" (d) (e) & \$ 6. Let , where is the function whose graph is given in #5 above. find the 1ÐBÑ œ 0Ð>Ñ.> 0 ! B intervals (if any) on which is concave up. 1 (a) (b) (c) (d) (e) none Ð\$ß (Ñ Ð!ß #Ñß Ð(ß *Ñ Ð\$ß *Ñ Ð!ß &Ñ 7. Evaluate Î # Î# # 1 1 sin BB * . B (a) (b) (c) (d) (e) 11 1 1 #% % % ## #   * ! # " 1 8. Evaluate by first expressing the given limit as a definite integral. lim 8Ä∞ 3œ" 8 Ð"&3Î8Ñ & 8  / (a) (b) (c) (d) (e) // (# ' & ' &Î8 / / / " / / / ln ln 9. Evaluate by using the properties of the integral and relating it to   # # # \$ %B #B .B areas. (i.e., do NOT try to find antiderivatives). (a) (b) (c) (d) (e) "# % "# "' ' "' "# ) ' ) 111 1 1 10. Evaluate 1 1 Î' Î% sec tan BB . B (a) (b) (c) (d) (e)  \$\$ #" # " " # # # 11. Evaluate # " # ' "> .> (a) (b) (c) (d) (e) *\$ 12. Write as a single integral in the form : + ,  # # # #&" 0ÐBÑ.B  0ÐBÑ.B  (a) (b) (c) (d) (e)  " # # # & &#
13. Let , where . Find . JÐBÑ œ 0Ð>Ñ.> 0Ð>Ñ œ .? J Ð#Ñ  "" B> "?

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## This note was uploaded on 12/12/2011 for the course MATH 1zc3 taught by Professor Mclean during the Spring '11 term at McMaster University.

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sample1 - Math 1ZB3 1st Sample Test #1 Name:_ (Last Name)...

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