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Unformatted text preview: Math 137 ASSIGNMENT 10 Fall 2007 NOT FOR SUBMISSION, BUT WILL BE TESTED ON THE FINAL EXAM IMPORTANT : 1. Your ﬁnal examination has problems on the material covered on this assignment. Do
the boxed problems now, so you have a complete idea of what to expect. 2. There will be an open tutorial on Assignment. 10 on MONDAY, DECEMBER 3,
4:00 — 5:00 pm. in RCH 101 (i.e., shared with your Algebra tutorials), to assist you in
solving these problems. Solutions will be posted on Tuesday, December 4. 3. Information about the exam, including a list of theorems and proofs to know, plus a
sample exam will be available by Monday, December 3. 4. There will be a pre—exam question and answer session on TUESDAY, DECEMBER 11,
12 noon — 2 pin, in DC 1350. Help will also be available on Monday and Tuesday,
December 10th and 11th, in the Tutorial Centre, MC 4066. TEXT PROBLEMS: Section 5.4 — 9, 11, I, I, 29, 31, 37, I, 43, I, 48, 51, I, 61,, 65 Section 5.5 — 75, 76, 79,
Section 6.1  3, I, 13, I, 21, 27, I, I, 45 EXTRA PROBLEMS: 1310.], Find the area. of the region bounded by the given curves: . ’)
a) y = srn7rrr , 312:5“ 2m
,yzQ—a‘, andw=—1.
1+.‘L‘2' — at, and :1: = 2. bly= (I:
E102 Consider the function 9(11) 2 / 6“2 dt.
. 0 a) Explain how you know 9(51‘) exists and is diﬁerentiable for a: E R.
b) Find 9(0). C) Show that
(i) 0 < (Mar) 3 1 for all :C E R, and (ii) lim g'(5t') = 0, and (iii) g’(0) = 1. [ml—00
d) Find intervals on which the graph of g(.n) is concave up and concave down.
e) Use the results of b), c), (1) to sketch a qualitative graph of 9(a) continued. .. 90?) f) Evaluate Iim —. x—'O 21:
v
E103 The graph at right shows the velocities of two Bank '2
boats travelling down a lake for 0 S t S 15*. B l 1 Which boat has travelled the greater distance?
Explain how you know E104 If f is continuous on [Om/2], Show that
~7r/2 ”IT/2
/ “COS 513) div = / f(sin :13) d3:
0 0 7r 7r
[HINTz Use the fact that cos a: = sin (a — or) , and then let u = 5 — x in the left—hand integral.] ...
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 Fall '08
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