MATH118MS06S

# MATH118MS06S - Faculty of Mathematics University of...

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Faculty of Mathematics University of Waterloo Math 118 Midterm — Spring 2006 Time: 2 hours Date: June 5, 2006. Last Name: _______________ First Name: ID. Number: ________ Signature: Instructors: [:1 /Chemical Eng. D. Wolczuk El/ Enviro/ Geo Eng. C. Hoppen El Mechanical Eng. P. Pralat El Mechatronics Eng. R. Oyono Your answers must be stated in a clear and logical form in order to receive full marks. Instructions: 1. Complete the information section Question Mark Value above, indicating your instructors A name by a checkmark in the appro- priate box. 2. Place your initials at the top corner of each page in the space provided. 3. NO CALCULATORS permitted. 4. Tear off the back last page of the test to use for rough work. 5 Math 118 — Midterm Page 2 of 8 Initials: 1. Evaluate the following indeﬁnite integrals TQM/a 5UESTE‘EKVQQM . 4 a “L d ,3 [ ] ) f W 517 (1:1 ﬁr:’?ﬁ‘g 9 [ghalech \ b1” dist: +0n35€09 X X Wﬁﬁ \ Subgwgn 3 “TVS 45 Tag SUbacomP‘e Siam/e 953% "anrh A'W‘S 5gb .hghs Math 118 — Midterm Page 3 of 8 5' powd ﬂaﬁhitials: ‘7? ‘ [4] 0) f 2%15 dm Uée Sub by (anWWEIBAg‘ﬂe SCLUO “3.: j“ QQer‘ve/ .30LKAOXQ Q5: QQHQM\‘mj%\’br “w '2. ,‘ yl—V Cy +5 @Qf’arﬁmwv‘ﬂ 4r\Y\ {V QLXWWWK QYN 26v h=O B: ‘ﬁl M6 K: I t \ muld’vwmmﬂt :7 W”) +‘ 0* bogs k I QNL’QOYW“ «£60 Q (ha, 2 Tam/1 5:4 1551 17pm om . ,/ A ‘ . a ><:(s"+omfr’ * b, Double meow“ (M S otih 9 * v' \ KsedHC/m 09 @Omg *’ 3 gﬂmg _ W d8 5* 0(3’9 *6 r :ﬁWseﬂGdQ/‘jp’i/ gngQ +3 r f ‘migﬁdg * jjga/ +Om8+5 % x \ I (Lsz d8 5 " ( jﬁiiﬁ “‘8’ * \n\ +Om" d&%g%o\9 4/ \h :EVNWOHQ *Lﬁgjr \h \sm :5 \‘(\\’§OI\EV\ Jf\‘(‘\\\$\ 1’ :@\n]\() Jrﬂy ’H “727%— A— ”Q) 2: -—---" 3 \7- M it: : i Math 118 - Midterln 7* 3‘ Page 4 of 8 Initials: 2. Evaluate the following deﬁnite integrals U = x +3 3 2x ‘ l4] 3) 0 «mdm clu=d><- mil—“Cghéxghj Math 118 - Midterm Page 5 of 8 Initials: b 3. Consider the integral f: cos dac o .1 , 5 [3] a) Estimate the Vfrlue of the integral using Trapezoidal Rule with n = 6. ﬁgzbflﬁmwae+§ﬂnﬂrt*el¢*l%ﬁigl <:; : L:l YE _ym i2 K .,_.——d- ’— :WBN 1’“; - w ﬁfe—g New“ * aé"*ﬁ\+_(—\+%l*(-l*% +(-I+%‘) >< _ \ y , 'ZT(—lr%l AIZ-Lml—Qzﬁ'ig ’“lél_‘“l / 4 m hie“7é“§ [2] b) Use the formula Error 3 gig—35):, where M is the maximum value of lf”(av)| on a S as g b, to ﬁnd an upper bound of the error for your A b estimate in part a). N1 we (1g) 3 M3 =/’”sml'i:>§lfll Err“ ‘4‘“ U2”). ~ “9’ / \DlQZ ‘ Nmﬂwﬂmw i 9* g1 9m) \QQQ li“”ﬂ_ 4 a? ” “Zia” , A, " r 2. C¥ \VlQX- > 'll /L‘ /_ 3 - ’ 4e ":50 (g I OR ‘L'XL‘7/V ,Tej ( Q03<Ea>+ A§((‘J~l.,zr)+,(( to) +44“; Ailrﬂ :LCO ZEEE + Aer +Q+\~> 3 3 "".__.‘ >4 ’— BKLLVB @434; m ’2 \ "'1; -x— 53:25) ’19 V _. ’2 Math 118 — Midterm Page 6 of 8 Initials: 4. Consider the curve in polar coordinates 7“ = 3 + 381n6 ’) [3] a) Draw the curve on the axis. Show all steps used to arrive at your graph. 1‘ [3] b) Find the equation of the curve in Cartesian coordinates. ,, a; 3* gnggi _/ g Y2 (@038 8 ‘2 k\: (S‘\\9 “‘/’M / A 7 l X” i D M “ \$33: :: A \I'i Math 118 — Midterm Page 7 of 8 Initials: 5. Short Answer Problems 1 [1] a) What is fsecrr dx? \ﬂlSQCX 4)va xlw <— 2 dX a 3;” - O, [1] 0) Write the formula for length of a parametric curve (30,31) :2 (a:(t),y(t)), a < t < b ‘m (/7 94 /""Y l” \\ L b / 1' 7— m - ! 2W~"":--~——-~~-~~, Qj Wm) M “N ” J1 \f‘xMHy/e)?“ ta 1 d What is the formula for computing —dy for a curve 'r = 0 that is in dz polar coordinates? ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 7

MATH118MS06S - Faculty of Mathematics University of...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online