Unformatted text preview: Math 137 ASSIGNMENT 10 Fall 2006 NOT FOR SUBMISSION, BUT WILL BE TESTED ON THE FINAL EXAM) IMPORTANT :
. 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. Solutions will be
posted on Tuesdav December 5. 2. Information about the exam; including a list of theorems and proofs to know, plus a sample
exam will be available by Monday, December 4. 3. There will be an open tutorial on Assignment 10 on MONDAY, DECEMBER 4,
4:00 — 5:00 p.111. in RCH 101 (i.e., shared with your Algebra tutorials). to assist you
in solving these problems. in addition there will be a question and answer session on
Assignment. 10 (or other Math 13? topics of your choice) on VVRDNESDAY, DECEMBER 6.
3:30 — 5:00 pm. in DC 1351. TEXT PROBLEMS: Section 5.4 — l , I, 45. 47, 48, I, Section 5.5 — 75, 77, Section 6.1 — 3, l 9: 15, I, 20, 23,
EXTRA PROBLEMS: 21'
l+$2‘ E101 Find the area of the region bounded by y = y = 2 ~ a", and I = —1. E102 Consider the function g(1¢) = f 642 (it.
0 a) Explain how you know 9(1)) exists and is ('lill'erentiable for :1: E R
1)) Find 9(0)
e) Show that
(i) 0 < _g’(:i:) 5 l for all :1: 6 IR, and (ii) lim g’(:r) = 0., and (iii) g’(()) = 1. :i:—>oc
cl) Find intervals on which the graph of {1(33) is concave up and concave down. e) Use the results of b), c). d) to sketch a qualitative graph of g(:c). l') Evaluate liin Qty). af—~0 21' Note: In applying the definite integral; it is in‘lportant to include a brief developn'ient of the
i1'1tegral for the purpose at hand. For example, in area problems, make a sketch of the region
and show a typical area element A11. ...
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