Practice Midterm I - 6

Practice Midterm I - 6 - Name Student Number MATHEMATICS...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Name: Student Number: MATHEMATICS 1A03/1N03E Term Test C. McLean DURATION OF TEST: 1 hour MCMASTER UNIVERSITY TERM TEST Thursday, May 24, 2007 THIS TEST INCLUDES 8 PAGES AND 12 QUESTIONS. YOU ARE RESPONSIBLE FOR ENSURING YOUR COPY OF THE TEST IS COMPLETE. BRING ANY DISCREPANCY TO THE ATTENTION OF YOUR INVIGILATOR. Instructions: 1. NO calculator is allowed to be used on this test. 2. Put your name and student number at the top of each page. 3. In part A, PRINT the letter corresponding to the answer of your choice on page 2, in the box beside the corresponding guestion number below. 4. A blank answer is an automatic zero for any question in part A, even- if the correct solution is circled on the question itself. Incorrect or multiple answers are also worth zero marks. No negative marks or part marks Will be assigned. 5. In part B, provide complete solutions on this exam paper in the space provided below each question. Part marks are available. 6. Each question in part A is worth 1 mark, and in part B each question is worth 3 marks. 7. Rough work paper will be provided upon request. All rough work must be handed in with the test, but any solutions written on the rough paper will NOT be graded. 8. Good Luck! Continued on page #2 Name: Student #:_________ Page 2 Part B Question I Grade #9 Total Part A: Total Pan‘ B: /8 /12 Net Grade: i 153‘ Continued on page #3 Student #1 . _ . Page3 Name: PART A Enter the letter of the correct solution in the; appropriate box on the first page. No part marks will be given for this section 1. Which one of. the following expressions describes the domain Of the function: I ‘n f 3) a" 7 0 i 9:70" 33567;; we; , ~ ‘3) 7/! a) (moo) b) [0,oo) e) (Leo) [190) e) (cope) .2. Starting with the graph of the function: I Sky; % Coup/w r ‘ P33 which of the following describes how to produce the graph of; g(x)=\/2x—l a) Shiftfl/E);99995?'Q.ni-t-iaHQ;-§tr¢t9h hoziéqngtallX-PXézfaetomiz-- -- b . hiftf 00 right one units?de sgnttacthgrézswmally .‘bry‘ afactor 0.22- c) Shift f(x) up by two and-shift left By 2556 “' " " _ " '_ d) Stretch f(x) vertically E‘ylfaét‘ori'o‘i by e) Stretch f (x) horizontally by a factor of two, and shift left by 1 Continued on page #4 (Hf?/D Name: 7 __ - - -Student#: Page4 I 3. Which of'the'*fo'lloWing is the inverSe functionofze - ~ _ Y‘ f(x)=1n(J§:_1)=y 9 e ‘ J3: ‘ 7.: I a) ——(——1——) b) e H c)";:e.J;_+_1 d) e‘E—e {fl e2‘+1\/ 1 H In x—l ' ' _ r fox/WV? mitt, We! 4. Given the function below: (On-f or L ) x+1 ifx<1 h(x)= 1pc ifle<3<—- Coh‘}"(3;3) g3: if‘x23 R can} V53 Which of the following is a statéhieht? “ ‘ ai’i. ’XH 2 13’ M29" t 5,1] Roi“ /rx ’3 M. a) h(x) is continuous everywhere. 0", fl, 1 . . = . . t :3. I __ b) : h()t) Iérléf‘} atJt : anci nghtcontinuous a x a r“ ’3' _, O c) hfx‘)‘is‘i‘ight"continu0iIS‘iitxé‘l; andileft'Con't'i'nuous atx’='3’. 2 ' - 3E ~ ' ' e) h_(x__)_uis ,Ileft continuous i 1 JE 37‘ I (6 ‘3) {01 Hr a} l Continued on page #5 & I‘Uz) 3- -J,,(.:g ) 77,3 11) a!“ raj-h» W1 Name: Student #:___________ Page 5 5. Evaluate the limit: ... ‘- W /’ 'J’ “ '2 7 '1. WC? 1* ~ 11m N (\ GD “’93: 1 j a) 0 b) g —oo d) co e) Undefined 6. Find the derivative of the function: A} .1 1w; [Zed ' la ‘2. 3.541% ‘1! (x 2" a) 005:2” b) écos(x) c) 1 xcos(2x)x—2%sin(2x) e) —xcos(2:)2—sin(2x) Continued on page #6 Name: Student #:-______ Page 6' ' 7. Which of the following is equivalent to h'(1), if h(x) is given by the expression: h(x) = em") “1-9670 ' )- e i x: l where the function f (x) has f (1)=1, and f’(1)=2, k {If (2- “(if :3; 29%?) l I : 6 ° 2 5 fer) ’ 4 2 b 2 1 d) 4 e) 4e4 [:11 e ) e c) e f) A,(’) » 14m , ‘3’ _ i 1,}- 1:1; 2 ’1’ 1' E‘» ___________________________________________________________ .- {e ,9 v 211 '/m “7 11/3; «9 f 8. Find the second derivative of: \‘M’ f(x) = tan—106) l a) —chc(x)cot(x) b) ~csc2(x) c) l+x2 M —2x. 1 ifl(l+x2)2 e) Z—x Continued on page #7 Name: Student #: Page 7 PART B Provide complete solutions in the spaces below the questions. 9. Given the equation: cos(2x + y2) = e’l evaluate 21—: using implicit differentiation. cliiPe/en‘l'id Lit} Sick; } l ' ' s >’ "Sin(1<7r+y1)° i;(l?r%y7'l = 8 ' Eff.) _ x _ 2} ‘t. \ v 1 ‘~\__,,// ) -—Sm (lrxky—L) ° [1+1W? -: e)‘ 62>, y’ folvi‘r Cur y'l’. — ~ ‘ ,1 1 fl i“ Y?- ;7 .I I I 1!,” £21,. {a 3 w 1L9“ y 53 ‘l ( 1WFY1,) \/(ey1+ If” min“; :7 y"; ‘ 10. Expand the following. expression: m _« lain/73H) - in we“) _- 149;) la {11H} "(/A’~l)ly\1gvih/9J;r) .— a... IL‘ [0(14'") “Of ihltf’lh'z ~13. Ind /: Continued on page #8 1/2 /; Student #2 Name: Page 8 11. Find the equation of the tangent line to the curve: p(x)= ex+2x+3 at the point (0,4). (Put the final answer in the form of y=mx+b). fl, -) It ' “ if I w 0 , ‘9 PM +1 p(0)»€+2z3\2 L, —_ Li y 1h¢+L:>/ -=~ firm (cg y ~y; : m 0x~7rfl=3 >’~‘I': 3/wvo) ' ' “3 hm” ) 12. Simplify the expression: y = csc(tan“l (x)) (xiv; 7 turning it into an algebraic function. . 8‘" 'e'f’ (9 $406“ of a 41mg :7r 1' 79. if]. . [9 s (“all )) .J-r- \ “mu—NW,” _. . . (j J—-— : M :7, {V "i‘fi'l I; ‘S\l\9 "-’—--——..‘_ f ‘ OPP or W O) '3’» C169 3 THE END ...
View Full Document

{[ snackBarMessage ]}

Page1 / 8

Practice Midterm I - 6 - Name Student Number MATHEMATICS...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online