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Unformatted text preview: UNIVERSITY OF WATERLOO
TEST # 1
FALL TERM 2008 Student Name (Print Legibly)
(FAMILY NAME) (GIVEN NAME) Signature Student ID Number COURSE NUMBER MATH 127 COURSE TITLE Calculus 1 for the Sciences COURSE SECTION(s) 001 002 003 004 005 006 007 008 009 010
DATE OF EXAM Monday, October 20‘“, 2008 TIME PERIOD 17:30 — 18:50 DURATION OF EXAM 80 minutes NUMBER. OF EXAM PAGES (Including this sheet) 6 INSTRUCTORS (please indicate your section) [:1 01 B. Richmond (9:30) [I 06 M. Ashburner (1:30) C] 02 R. Green (10:30) El 07 B. Richmond (11:30)
El 03 P. Smith (1:30) [I 08 M. Ashburner (10:30)
E] 04 M. Best (12:30) D 09 .1. West (10:30) El 05 M. Calder (2:30) El 10 R. Green (8:30) EXAM TYPE Closed Book
ADDITIONAL MATERIALS ALLOWED NONE (NO CALCULATORS!) Notes: Marking Scheme: 1 


 m
 2
r0 1. Fill in your name, ID number
and Sign the paper. 2. Answer all questions in the
space provided. Ask the proc—
tor for extra blank pages if
necessary. Show your work. 3. Check that the examination
has 6 sheets. 4. Your grade will be in 
ﬂuenced by how clearly you express your ideas,
. Total 0
and how well you organlze
your solutions.
’1. \ '1—
00521 = 005 1’ 3'“ K 25m»: COSJL II SI’AQJL
r) (“Fusl’ calwlus (es—l a'l universI(yﬂgiHs) [2] [6] [6] MATH 127 — Test # 1. 1. Fall Term 2008‘ Page 2 of 6 a) If f(a:) = :1:2 + 1, evaluate b) Solve the following equations or inequalities.
(i) la: — 1 < 2 (ii) 6” + e"I = 2 0<x<27r (iii) sin 2113 = cosm, c) Evaluate the following expressions, giving exact answers such as %1n 3 + W.
(i) 111 e2 — ln2e (ii) sin—1(sin (iii) cos % [ii/inf: Wrife 77; as a. dl'fférence of S/oeci‘al ans/esj [4] [4] MATH 127  Test # 1. Fall Term 2008 Page 3 of 6 2. Consider the function f(x) — ln(:z: — 1). a) Sketch a graph of f (x) on the given axes. 3 b) State the domain and range of f. 0) Explain how you would know, from your graph in a), that the inverse function f “(x)
exists, and sketch its graph on the axes above, labelling it clearly. (I) Find the equation for f "1(z). MATH 127  Test # 1. Fall Term 2008 Page 4 of 6 3. Evaluate the following limits. $2+2$+1
2 ' ——
H a) 2+1
J2
[3] b) lim a: +3 z—wo 1— 2:1: , I 4 — a:
[3] C) $11.32 — ﬁ
[2] d) lim e"I 0052 at E—‘OO MATH 127 ~ Test # 1. Fall Term 2008 Page 5 of 6 4. The Bay of Fundy is reputed to have the highest tides in the world, with a difference of 20 metres between low and high water level. Suppose the depth y(t) metres at a particular
place in the Bay is given by y(t) = yo + Acos(Bt), where t measures the number of hours since the ﬁrst high tide on January 1, and the
constants yo, A, B are positive. [5] 3) Sketch a qualitative graph of y(t), labelling yo, and the amplitude and period,
Hint: If you ﬁnd the unknown constants confusing, just try it ﬁrst with numbers, such
as yo = 10, A = 3, and B = 2, for erample. Also, the meaning of amplitude is
the ’size’ of the oscillation from middle to top, i.e. half the overall change in y—value during each oscillation. The period is the length of time that it takes to undergo one
oscillation. A3 [1] b) What is the physical meaning of yo? [4] c) What is the value of the constants A and B, assuming the time between successive
high tides is 12 1/2 hours? MATH 127  Test # 1. Fall Term 2008 Page 6 of 6 [2] 5. The signum function, which is used to indicate whether a number is positive or neg—
ative, is given by
S n _ 1 if at > 0
g —1 if :1: < 0. For our purposes, this function is undeﬁned When .’L‘ = 0 (although most texts deﬁne
it to be 0 when a: = 0). Express this function in one line (i.e., not using cases) using
the absolute value function. You may use the space below for rough work, or to continue any other question
that you have ran out of space answering. Be sure to indicate clearly, in the
original location, that the work continues here. ...
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 Fall '09
 Prof.Smith
 Math, Continuous function, Tide, Fall term

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