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Unformatted text preview: George M. Bergman Fall 2008, Math 13 .  . . 19 Sept, 2008
155 Dwinelle Hall First Midterm ' 3:10—4:00 PM This is a closed book exam. You are allowed one 2sided 81/2" X 11" sheet of notes.
Attempt all problems. Write solutions on these sheets Ask for scratch paper if the
fronts and backs of these pages are not sufﬁcient; put your name on any such extra sheets and hand them 1n with your exam. Credit for an answer may be reduced if a large amount of irrelevant or incoherent material is included along with the correct answer.
Questions begin on the next sheet. Fill in your name and section on this sheet now, but do not turn the page until the signal is given. At the end of the exam, stop writing and
close your exam as soon as the ending signal is given, or you will lose points.
Think clearly, stay calm. Your name Sections: Mark yours with X.
(Note that they are listed in order of hour, not section—number.) usual place, hour (MW), Sec. TA
171 Stanley 8:00 9:00 201 El
3102 Etcheverry 9:00—10:00 203 E] 71 Evans 10001100 204 El Benjamin Tsou
3111Etcheverry 11:0012:00 205 El Harold Williams
75 Evans 12:00 1:00 206 [Z] Koushik Pal E]
D
D
E]
El Benjamin Tsou Kiri] Datchev 70 Evans 1:00— 2:00 207 Gary Sivek 105 Latimer 2:00— 3:00 208 Gary Sivek
3102 Etcheverry 2:00— 3:00 211
85 Evans 5:00 6:00 210 Koushik Pal
Harold Williams Other or none Explain Leave blank for grading
/ 36 FAMILY cincﬂs 13.1 Keane _ “Mr. Pizzarelli gave me his old guitar string! Can I learn how to play it?" 1. (65 points: 12 points for each except (d), which is 17 points.) Compute the following integrals. work answers:
(a) Ixe’zxdx (a)
(b) Isinsx 0036de (b)
'(c) I ”/4 tan 2x dx (0) —n'/4 .(1, continued) work  ‘ answers:
‘(x+ 1)2 (d) I x2_3x dx 0 0 , (d) — 1000 ._
(e) J._°:/ X 5/3 dx V > (C) 2. ('20 points) One of the formulas in the table of integrals in‘the back of our book is: du
25 =mm+4¢+w)+c.
J.«laz+uz
dx Use the above formula to obtain a formula for J ————— , where p and q are real
J}? + px + q
constants. (Hint: complete the square.) Indicate what inequality p and q must satisfy for this formula to follow from the formula given. Fill in your ﬁnal answers as indicated at the bottom of
this page. Answer: I —d—x—= 4x2+px+q Inequality that must be assumed 3. (15 points) Our teXt states the Midpoint Rule:
jabﬂx) dx 3 Ax[f(3r1) + +f(in.)], where Ax = (b — a)/n and X, = (xi_1 + xi)/2.
For this rule, it gives the error estimate saying that if If”(x) S K for a S» x S b, then
IEMI s K(b — a)3/24n2.
Compute the bound that this gives for the approximation stinSx dx
0 21 (2/100) (sin (50.01) + sin (50.03) + sin (5 0.05) + + sin (5 1.99)). Namely, if the above approximation to the integral is denoted M, determine numerically what
range of values around M the above error estimate says that I: sin5x dx must lie in. Use the
exact value coming from the error estimate, not a decimal approximation. Fill in your ﬁnal answer
as indicated at the bottom of this page. (A
/\ 2 .
Answer: I0 sm 5 x dx _ ...
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 Spring '08
 WILKENING

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