M137.F07.SampleTest1

M137.F07.SampleTest1 - Faculty of NIathematics University of Waterloo Math 137 Term Test 1 Fall Term 2006 Time 4:30 6:20 pm(SampLE TEST FDR FALL

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Unformatted text preview: Faculty of NIathematics University of Waterloo Math 137 Term Test 1 - Fall Term 2006 Time: 4:30 - 6:20 pm. (SampLE TEST- FDR FALL 2004>Date: October 10, 2006. AIDS: ‘PINK TIE’ CALCULATORS ONLY Family Name: Initials: ID. Number: Signature: Check the box next to your section: III 001 B. J. Marshman (11:30 am.) :1 008 S. Sivaloganathan (10:30 am) Cl 002 O. Winkler (12:30 pm.) I: 009 S. Gupta (2:30 pm.) D 003 L. Marcoux (1:30 pm.) III 010 S. Gupta (1:30 pm.) I: 004 N. Spronk (2:30 pm.) [I] 011 C: Struthers (9:30 am.) El 005 B. lngalls (1:30 pm.) D 012 D. Harmsworth ( 8:30 am.) III] 006 D. Park ( 9:30 am.) C] 013 D. Wolczuk (8:30 am.) III 007 Y—R. Liu (10:30 am.) [:1 014 M. Stastna (11:30 am.) Your answers must be stated in a clear and logical form in order to Reference any theorems or rules used by their receive full marks. name, or the appropriate abbreviation. Useful abbreviations for this test include LSR (limit sum rule), LPR (limit product rule), LQR (limit quotient rule), LCR (limit composite rule for basic functions). usequ trianghs -. A Note: 1. Complete the information section _ above, indicating your instructor‘s name by a checkmark in the appro priate box. 2. Place your initials and ID No: at the top right corner of each page. 3. Tear off the blank last page of the test to use for rough work. You may use the reverse of any page if you need extra space. 4. Any 60 marks worth of questions constitutes a complete test. MATH 137 TERM TEST #1 PAGE 2 1. For each qualitative sketch in this problem, explain clearly how you obtain your graph, and indicate all asymptotes and intercepts with the :L‘ and y axes, if they occur. [4] a.) Sketch the function f(1) = la” — 1|. ‘5 'x [4] b) Sketch the function f(x) = x2 — 21 on the upper axes, and then sketch its reciprocal 1 1 on the lower axes f (m) :52 — 22: . x 4% jg 7r . [6] c) Sketch graphs of the functions f(:c) = 1n [3:] and g(x) = tomb—:5) on the interval [—1, 3] and hence determine the number of solutions of the equation f(rz) = g(1‘) in [—1,3]. ‘5 y- . r I: no 0'] MATH 137 TERM TEST #1 PAGE 3 / 3—- — ._ ‘_—A./ / Consider the function i5} 2- a) 5: Eartha: = earctan I with graph y = f[:1:) as shown. (i) Use known bounds on arctanm for x 6 IR. to find the range of f: and hence 5" determine the horizontal asymptotes y = a and y = B. -11 E 5 :4 = E l?" 5 = (a = e"’1 3 (ii) Find the inverse function f“1(3:), and sketch 3/ = f“'(:r:) on the graph in a). E 3 a Tom (On xi] [10] b) (i) Use the identity cos(A+B) = cos A cos B—sin A sin B to prove that cos(2t) = 1 —2 sin? t. (ii) Sketch y1(t) = 2 + sint and 1,126) = 2 +005 2t on the given axes for O S t S 27r. and find the coordinates of any points of intersection in [0, 2w]. [CT/EiS/ZBI (532: 5/23, (37/2 ,0] I / {AH/M (iii) If y1(t) and y2(t) give the distances of two masses from the ceiling at time it, when are the two masses the same distance from the ceiling? ‘31. ‘5‘ MATH 137 TERM TEST # 1 PAGE 4 3. 3.) Evaluate each limit, or Show that it does not exist. Justify your reasoning. [3] b) Solve each equation or inequality. [3] . . :52—4 [1) z—2 (ii) — cosx v9z“ +5 (iii) lim z—m213+I+1 (1) 222 — 3 = 62‘” (ii) cos(arcsin x) = SI“ L43 i.” “’21 [01 [M51 E(‘:x<ll MATH 137 TERM TEST #1 PAGE 5 4. Label each statement as TRUE or FALSE in the blank provided. (Use the space between questions to justify your answer. Guesses will not be graded.) [3] a) The equation tan as = secac has no solutions. [3] b) __ The domain of f(x) = ln(arcsin z) is the interval ——1 S x S 1, [3] c) The function f(:I:) = ln(e“2’ - e"/‘) + 005G;- sin(%)) + log2(41) is constant. [2] d) If f and g are odd functions, then the product f(:z:) « g($) is also odd. [3] e) If f(3:) = 23: + lnz, then f-1(2) = —1_ [3] f) __ If la: — 1| < 2, then [33: + 5| < 15. ...
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This note was uploaded on 01/25/2010 for the course MATH MATH137 taught by Professor Oancea during the Fall '08 term at Waterloo.

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M137.F07.SampleTest1 - Faculty of NIathematics University of Waterloo Math 137 Term Test 1 Fall Term 2006 Time 4:30 6:20 pm(SampLE TEST FDR FALL

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