New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Math 32A (Hendricks) Final - Study Guide

by: Robin Zhang

Math 32A (Hendricks) Final - Study Guide Math 32A: Calculus of Several Variables

Robin Zhang

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

includes all sections covered in quarter, which is: 12.1 - Parametric Equations 12.2/14.3 - Arc Length and Speed 13.1 - Vector Geometry 13.2 - Vectors in Three Dimensions 13.3 - Dot Product an...
Calculus of Several Variables
Study Guide
50 ?




Popular in Calculus of Several Variables

Popular in Mathematics (M)

This 17 page Study Guide was uploaded by Robin Zhang on Monday December 7, 2015. The Study Guide belongs to Math 32A: Calculus of Several Variables at University of California - Los Angeles taught by Hendricks in Fall 2015. Since its upload, it has received 116 views. For similar materials see Calculus of Several Variables in Mathematics (M) at University of California - Los Angeles.

Similar to Math 32A: Calculus of Several Variables at UCLA


Reviews for Math 32A (Hendricks) Final - Study Guide


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 12/07/15
/VJ Sq.Af~'-tv t/vlsF.a1tJbU. ~tuy~bd<Q-b.l\.~a"j 1 12,IQoce Vfb.b'r 1 Arc /e,3U~ fro.<>lo~ ol£"'-h"(c LCi)y~/': $"=f:fy'(l--y'(f:-J"t--,e)./- -::f1/rU)cl£- \SI\v~ C.e(YV>ft~ If F(c)-<x,l!\,0> 0'\tc( ~-)-.1-Y•{I-)> C<l'f,V't-r.Jt>r>l~ \ ~Ie'"r fV!y \\\? L+ll(flj/( 11 '.J,kJr"lt,vt<J.'1-1.">k~ e-U,.a-. Uc.vk. V""C. "..h.Isot '"t.LI ~, 0;§/wbeJv.-1(t1blC1),.,Q. C"111L.,_) : P-GL=-S(,, •l-,-.,,(c)c~' ~o WweC " RIy.I~l<0,/.lho(-P,v<P,w >S-e CeAtna->8""'I~A (~b,o) : fqUt>IC-~[_,,"e, \'Ur;(.dv'C'C:I r( ~(y_tVo'b..,f!.6,c...'> 1 r~ ..£ct~< o-t5 ~-o') (-y.~ba< -<--.o.,.-~'c.r ;(l-i)p<il-,k?'.._(""'l>l"•f(JPS,'f-e )lopo.v ~ ~WH1l-ll- e-«e/1.v o."~i""c" f.v"""'*'" k- "t,_()1 )-e.YeN>eaJ.dJ.t~ >olvhr ~,..l-~ \.oLlf-Y\~1..l-e.-se- )CfL'akr tl~-~e\~. "7ipuf»'~ otovkv -lo~j~?-l !Mf)'~f-~0 ~0 l j k ~ tJ1 Ct- (.{ b1.~C-. VXw..::-w XV' ~ca frl:r0-{xYo+b(yyJ+~ (-b)-0- ax+b+cc-=d (a,l-) tthe.orMUvukr- J..ofh.e{a""'pp/ni) h~l tq""o,-P~eU;~ ~-.r/Jo:nl-.5 ~ Ao~ vec. t~, vove<JrLw;tt/vpoJM.-sJ U}epo;ttl-!l~>vJ.onJ.~t plO/lt- ~e vWcrvalued~o- r-,.etf~~ f"\OV;"~';,d- \11(/)I{: 9orOtv'ebh.cAl'?15"{.- il\l-trsecl'OJ5', [{0~ocJ sve.~-otre-v-CtnIlplI ~J.ooft.v eu.f..r'ufb7-..f-X:CvJt, 1 econ.fV\eltvrCVl-vt'l xtevty11.y-04~ we a lv;gt>"",dr~elY CL <>•s'."e'!)~- f;F{)~)(~' t (~(~~y{lI-&t :{f-)> -=I)~ o(~('_ t1JF-(t-U)IA r L"/---ct;- ~o A :: (x'(t-y'(f), l/{f--)> ~t-tles C(,U)+r\ltll' :'t-)flL0J ({}Ct():c rCr-)w-Gl\y (,o(-c~61) £(JCtt)()~:t'(t-),)'t(-~~~) k-?r~ Rvte * r&jet~)r{jU))3(1:-) o.[~- {.-Yi<5 DolnVl-o?r6'Au.J-5 F ];/{7'/J)~=j}xtV2_y' -~rc'-f­(~r-) ~,t: It")'1 A-r--eYpfort~:l""'e-~?v-1-.<n So!vI114~ ~1 ~ f.v.oPti-..,_ 10 {lt,'>y"~<l1.fw..dv'&n "{- pi f~;ver>l.w'~ 1i /.on'j'l:v¥n (Ct-1-gu-?[sCs'J) ~ .tJ.#srr U11Tu:1efuftU-rM:,,·tl-)11 ~ J<isI*II "'-1s/1-r'&)/1 0(p.~ ~v&(Mc.J..t:n o{C(~~ 1(x) ()_)~0:: k.1how Aoh''~te{;l/..\ofo~'~ 1 l~(sL 1~1 1Mu;/beg~ /fw01 SCfeo,:,- fVlu}()/Yh~tkor~ue1-,:0 deiitt.e-.Cc---."b.I Verl-.'!.4l Tr((.ce5 .•. IIKeplu,)=G4. c01k:a1p~·" ka,1{{rA,y)) IIJ{(J~ y:b (Of'lC(/1 (J&~b,/(x/o)) Hotn-~Tq(e5,. • J/kep~t:- c~.L ulpoi {1'C-1)SSud,~1- ~(y, y) vt":l{l~s oIeve0.<I'~ CPrvC:'~C~l,1,l'plw-e ~ 0'\-t'Mt .fice5fN/"1oa t'x-Jz} S11-uvll, T1hvodwtveA{x-l) 1'~~lt,-e{1J ,; \)/.((Ct,b(x-f-{y-b?S/1-zall cx:;p[{,~L /'(- OlC>0Iharexs)b>0 Suv~air r? {~Cth'e-S l~, ~c.rr~if((~,(·) 43{)~)M vo~s1- Q SUMla.r cr,1J~ /1r11-[,,c.;(p) (iC~J u-,-k'/w·1xfwCl{) G) ProJ.-(,1(f{·J(,yo~Ctp -(x Jx,)})){x,1}:;p ® Ov~;:(..~ ~f j{x)~0, yl.~A ()y) -rf;p(Lf) (>c,>(y).-bA- \ &,PJ{xYJ [o/u,'I{~~~ f:y)tSCCYISC(l~b) ;.{. 1 1 -~~- 'd-~(lCllCO"l-l;Il'~ ·; ~A r.YJi~~'-! t~vrYfO"ra1;I' -s &~~"' Ttpsf~;>~vuMil.:§ 0 Svla~fth...~ -t.~ LAL-kCx(l,-Lh'-1-o1CJI(JloCbJ"~ fho~ /~{fxf~ ~("~=~>:(ub) i{CG_/,i~oprodug{1>-5~, {_;.1 J•e"rS L"tv'l1!~21uk he /'L'----...J ~~I-,\~LC/\C h~{.v)~oi_,C(('~-co"l~/l~A:ous cd~- (abJ ~ C{~(l L((~Or)~lJ{,->tvo~J 11 G)lJ)(\)cJ.(y-X'lJ.)li' IS~f~ ®l.he¥"'coor.tlC_)(>rlV=-r~~""") @ ()~~he,v!t-\he?r~M Pu. \ ct\'~ie~Ctr-fTA.efe;0f-vltv;gLJ}~HJf&1- Jo (!CtV~HI(I6Se.pcrt.-ld.y }(l'tJ~ +lA-v~n· ,sfo~e eMtl b +tLopw1-1'" cteA~Hve-~ lo SDlvepwl ·itJty{.,c t,Clten',0tlt~kf~ Jowtal-e-vVtVfohte- (y1{orrMO /1Q~ -~ fA!}IeJ ~Y~Ie, ~Y(x'Lys::2xy~ -€~ ys-i's CMfl.tnaJo-7L X s 9~t14-cl:\ ed, 0~n t\u[eCjA, ~r tr'v-fobleVkkeveno~ ~ 1 ~Vul Ct~(_'?-". e'NVtJ. ~) (~((x"y'lJ)5x:''-Co()(y") Th.e{JC:>/Je~te-s-j.:Ite..k.~~ hr ~ /-042-­ of.- tfra~ orr:kr... C[oi l~Cllv~-Jr(-xy GHLv.-yC'ru,,-cc,~Ac s.J.<:c of\cJJD-<}-~( C)y;lyy 1 1h\1by.k,~o~.orJ..G~e1'f.- "-1~c:~>ri-te.t}- ~ ~,vU(.o~~/'e/'1~-~ Yo(.\ c)JfkreAkvv1-I'~C~h,UvI-o k~, Re.H-~rira\ - der;vul~-vv~en~pJnM-"'-~e. o.0>'1 1Y~C!Ike.. r'\,VMeThe\'5-t~-t-~\(>>r} w1ttJ.-~h.fv-l?-f~a:' ~.eL.-hnl~" c0\ .1./()i'~i ~>rT/'A.-i o.A~ U-~cy~I,tou-~~~~e~161~ rt-~t: p-J~/5~ ~~ C1b)-ty(a/o)C-.C{1b){y-t) L-. A-f pro'( Ca+.61b+bay~ )~et.,C1bh..-+~{a,6y /).~({-~t{,)) 14 B"'u t-;-.-~~ ~Ix,,v) 'il{:fv("'J1{u,b))laiupp ~1vAtri~61e;) ~~ (\~-~, LH ta ol;{ferel/m·'0,l{Yie VCU~'~t.tbftt UW1(1tfoP"r4s Tf f ~ :(Aa.rJ,!~h ./fi.1 it(1U)vi-t.p\(r-) -itc> (-{;¥r-,))<~xv'Mt,~'r), -Jx£f-~YTt-&?rb- De"o\DeAv-tbhve? ~"3 \,h>Wreo-.oSfiU'P"'""it..e. 1Akrl>M.~>c.l~ <J1'4~,.., 1lo~ <>-<k_riv\)p(?)o~--fl-(J ;II ke~t)'d-a ii ~ e;;1c~0 "1~11 J->fp~mV N' e:-1C~/ \"o~p< Je<«"Vfrf'A,I";~ \~ , ~ rs\l-k ~" Cwv""'-P" r"i ,y. ~.\"'.L4)~ fcvJ k.ckPob~ V~,(x-u-1e--c0)-=- ~~l12)x-ayc 1Zl-~4r(a~:~-0 0 LekXy1;l,ot~~ ( v .,5-nA!/;­ c)(7)((YoY(JJIo2( _)~, ~ ~()(1y(ss,0~{s,0) \s(__p CYSh.hO'>t'h~ TtLfo0U'eni~c? srP"".~"" l'ct.l;"il ,!:~vH., FCx,y,:)-:: 1~"~ "I~~ ~-!ovtXiYfaYP~{o,t'.~ o~Gt :)r: [-("{o{1h)furC1'f)D(r) ~ou.""'.,_.,... [{y,>}C{a,{.al(r,&V(p,r~t-f/>#"""~"" &/hlR(orJ..­ Apo- P:=h-IV\hte~~ o~ t{¥y)ia Cnbtp~/(/{:1,_ txc,,t0::~r r'),f>)dDesh¢-e- xO~f'lc.< (y'1b-=0 or fy a;'orbeJ11o~'f-J 1 Fcr~ ~,erI-- rF ('l<~}f()[e>c.lor P=fft..{_a,,) a (AJh'f~. o~.t(Jy- ~eu> O1·Av~lhtrv{. O= JtxK[t:t,fxy(b)J f-y{C~. f-yo1)) II- 0>O1 f-{u/o:>0 tLa,b)IJ~ }eu-MJ/1 .ff0> 0Itxx (ul(0 ~L t),a,a l~t ~t f{X 11-0< 0 Mue tretS«clipo!J·l-{a,6) 1 .1JV-C1 kl1-/rttCcl~~Oe- Cvto t~>e.drt-~ £'rs~&. \{_~1' I- \o~ c \ ~~AJ o/,~~ GJlYSoh'Yct5k?Jl""'$riZ,£1A boVI'Id.on,5 aU L"}e;(;r-;(~'brPOl, i"f'l~y)/-oro cAuK vnhiey;>o:'-t~ ~ boV\.dc~ies V1' ~su c'£,.f.ry~'~ MW/r +-._,~J(.J,Je ?, {-;J.J~P3J,!,."ee&.fu:> fl/\)~~t_~ ~~ of= Vk,bJ1\ -ltflrJi.nJ­ clrr(e-J..~~ vv~ :o{ ol-fh(Pl' (vrJ'l-- AI-c~ l-wteacM~eA wet.'-~- (>lhy; CIYl&/-n;J.;v..~~r~e t,l¥0~ ·'vt-J..-(1v,C V~c \..-/t 1,~~e ..u.- w,-t-~J, \1ci$ ol ~ o~~~ h./{e C0'\~6\.ue Yo...,~!{ecSys!e~( eu.l."okW se.111(j ev&yLo""'f'of'ile.qw~o~ r<Y(l~ Co"" .1~\1M...lfb'f~.Yo«'-"afJ.<> u5e~..(pt r\~J~()Jo4Lp.


Buy Material

Are you sure you want to buy this material for

50 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Allison Fischer University of Alabama

"I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.