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


by: Moshe Swift III

MultivariateCalculus MATH200

Marketplace > Drexel University > Mathematics (M) > MATH200 > MultivariateCalculus
Moshe Swift III
GPA 3.63


Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

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

Class Notes
25 ?




Popular in Course

Popular in Mathematics (M)

This 18 page Class Notes was uploaded by Moshe Swift III on Wednesday September 23, 2015. The Class Notes belongs to MATH200 at Drexel University taught by DarylFalco in Fall. Since its upload, it has received 54 views. For similar materials see /class/212277/math200-drexel-university in Mathematics (M) at Drexel University.

Similar to MATH200 at Drexel

Popular in Mathematics (M)


Reviews for MultivariateCalculus


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: 09/23/15
Lgcvune 5 Motrinmeme g cm wws mum D Mvmvec fun ch39on I rial 11 J 04 5 q k I w J 10 Thquot Shun A P I d Appmxl39maI39cm anml 2390 M4029 gm rt 1 Af rm Owl U STION How Do we 39 mm 0 muz Tm ON meme 2 if ank iM g W m z jm Mo 34 Bx 57 Ax Pctth n M quota gnaw 404 34 A 3 50 Ex 39x 30W v as o tond39unl bread 1 as Jim van39ahu r E I x E 0 AP A J39Ag w x n an 2 Mn nthpom x v o x 019332 sun I 1 7 3quot quothapm AP um A xvir1 our Hf 39 1A 17 quotP inquot t V U mn n V V 1h15Kh o f l L39K1 j ndwmc3 0quot 9 Vm I no w 3 Vang APP yleam 3quoton luff F We Cl la gx X M 7LAx 3 think J h 4 U 39Uh39j 4140 z 7 Ax 47c FOK M L o m THfT m7 PULW H45 F 0 5quot 13913 I43 tj l 7 L 39 530 VQC K3953 2392 79 Lon an gi x wph L2 35obojquoti0 A 75 Low uvu Niel 32 L a L mm 50 24 in Mac Anny Plume h M Mrafou OJ JAINquot To clvhu 4 4393 dzlu mM39M A pluM 5 5 a 4 a Xprfo 4 baf e 5 339 1 Phat V J 39quot drum uquot i a39uah39ou Ifth M1 43 l MO 5 LN 0m WU aw TM a m Hon urMulac 4 sazm ugfgqu g dose g VN aw Inf ch WM mm uw39om APPLICATION 07 PARTAL oneVanni L omlwzmou Pzomsm To inc MiniMuMMuwwuw a an umch u4 A a load morvum39mum v11 39 j s 39 mm 5 Pk Also nd39u 1oaxxw45vjv1 Exchad b43054 so 0070 Iggf39o 5 5 4 cunt r 00V 5 50 O 40 5 5 Def MHW 7 A 39s Q CM HCM NWT off WW 0 GnJW3wol jb6 XOMV 3939 x2 2 913314 X39 M 39v r a v av gquot Sow nowz 39 quot 39 98 29 3342 2 x w 39 4390 2x z52 7t Viu at 2x 43 24zx 2uj 02146310 2 3 63 2x 2 RNA 4 4k vih td po u and So Sex at an US 0 an 2125410 mw so 2quot S 150 a My Mo uni0 5 O E Q mmmi P quot quot39 39939 22Co4230 Bfw a z z I 3 v I 39 x 39 em C n ud pomk C4 0 PossiBiV 39 T ME Cad OV39 Ln 1 he 9 N n NMM 9 Mammuw quot9 Sc d How 0 ilk Mi n1 1 inky 0 AM My you who un na 2 In ux I T Vs quot don Ma s 3 2 P r I m 3 41423 WWW uR W 3 l CHAPUL 3339 LOCAL LIAMn APP OYIMA IIO Se LEVl m M tuh A 139vt A a v Whit 7 90 n Cwem in quot It I he 8 can a Annoy 4 3 539 C X 5 quotcm x r 0 a Ur S MM Loud Linear apymx 4o 3 ad 1quot TN 8 05 d au V 7t 139 to cw 7 Hn nA Ha ft m r in Ir J 72 wt x Lc 7czxoAx 4hcn W4 howl 1413 9 H71 4 39m 011 App LYING LLC To rumn om a ri e nu mm c EEXAMPI e w 4 u y 5 A C 7 I 5 39 v5hh39139 439 I39r39 x A 4 ts JR LLC m L Q39j 439 050345 5 JN X 163411439 7 a l3 1o1AL bwrutg x 69 Wonk BIANPLQS ON LOCAL LINEAK APPPDWMATIONS CD FFEKCNTIALS We 39 8 z 0 w 39 A2 39 73 ABme i wm 39 3 504A mauncm Ewavupu ApproxM052 90 2quot land SOLuA Cw o 5quot39nlfi 702k31 01 950314 51 outt ij0oL I jquot 7 L 1 1 L WE9Ww M3 WM WW MT7119 a x 2 2 quot 13 5 39 rip c f 3 1 lt L I 5 13 3 Hwy 39 474 3 m2 3 3 139 1J M s APVmA Emma LL39xopkgy OAM9A3 5 ECGOngwod quot ltlquot0 39 rLa a3 a a S N an wake iwmms APPUCA DON MAN PLQ CD The L603 0 CL v39c dugud 4vvuv 3 4 are measured 419 be 3cm WW CNS bulk CK WM Wtqou mum mar 0L OOSCN I A rack mzasummmk AppmmiMuk HM Mth Wm paggibm NOV n 4W Arcq P 4N n avt Lc goLJK cio ack 1 a mtp quotr me Xw 394 I XSO M qn3tw5r meM OWL ca 4nd d fro Hawk 50 Wci M 5 LWW I 103CM 44 1 39 Kox up M Q WCQ 1lt19I oow r K i 1 2 1 ch 3 27 7 1 Q quot2 QMWAJ l 00 4 0 0 LNQ39gtI 3037 71k l7HV PA T IL FIND APPROYM 39TE MAYINuN Vosxlm zgznatt IN A EA 1mm 196 o 7144614 MAY WSWfat 7 Exam 00164 le 39o r L5 0 Abx 35 Limo 4315 am 5 4 CHAPTER 3 4 SIGNED Hothakk CALCULUS EArLL l TxArvscangmrAL qT DITIo PA Ga 74quotquot 2 l q A mum q qC3cl3qs f 39 LU 2x j39q W l 2zo 3143 iquot01 nna 44ml LLA 0 Um Spea39xl39ec EngHon g a Paan P CDNVQR JAM rmr 39r a mximah39ncr 53 L a 4M speci ed VOCAt C5 budH 44quot Al39shmu 5M4 Panel Q Ab x 39A AC X0140 1 39 22 L 3 kt wquotjigz 413 X LL Hill2 439 t 9 39 3 11 new quot S 8 mpc w 3 3 MWquot W n 4 50 Law g quot 4302 3 owm 49 01004 Q39 7 l J l t39 i t t l l i l E rror 39 39ib 15 3 3 4 5 6 7 8 tma l and 12 that V omen enema EMEREREES mm 13 4 Dilferenttability Differentials and Local Linearity 94 asusjlstqg zg 0 Use De nitions l34l and 342 to prove that a con stant function of two or three variable dil l erentiahh ex erywhere Use De nitions 34l and I3 4 to prove that a linear function of two or three variables is differentiable every where Use De nition 13 j to prove that ft39 y x3 2 2 is differ ntiahle at 0 0 0 Use Definition 342 to determine all values ofr such that fx y z x2 y W is differentiable at 0 0 O 15 16 17 18 19 u 20 11 1 l02 24 fx t Q 009198 25 fry P 12 Ql099 l02 26 y g i 2 4 x Q l04 w 4 iii false Explain Z7 By de nition a function fx y la differentiable at 90 to provided both fx x0 yo and j xo ya are de ned Z8 For any point xov m in the domain of a function fx y we have ii A aaiht4ca vw l39tll 4w r u r 12 1 9L 5 e I at t 7 I a4 i ll Ii 13 l 1 I frat i II A r 4 arr Axe 3139 gt gt villi 1 39 lhx I llIIA u vlus 39 liarta I t Lama L t V 39i V ax Aliquot 948 Chapter 13 Partial Derivatives 3 In the accompanying gure a rectangle with initial length x0 and initial width yo has been enlarged resulting in a rectan gle with length x0 AA and width yo Ay What portion of the gure represents the increase in the area of the rectan gle What portion ofthe gure represents an approximation of the increase in area by a total differential l L A Figure x31 32 The volume V ofa right Circular cone of radius r and height I is given by V rrr2hu Suppose that the height decreases from 3920 in to 19 95 in and the radius increases from 4 in to 405 in Compare the change in volume of the cone with an approximation of this change using a total differential 3340 a Find the local littear approximation L to the speci ed function f at the designated point Pi b Compare the errtir in approximating f by L at the speci ed point Q with the distance between P and Q 33 ft y P43 Qua 30M fx Y Aftquot Ptl 2t QtlDl 2 02 f39r i Z rye t y A Plel l l Q 09 099 101 yz for Z xev3 P1 l l Q0991 7 0 fivt z Intx v2 Pt2 I JL Q0 02097 l0l C f1xtaz 2 l X4 Kil2x y T l r ximation of the function li0 r l l fy l in each part con rm that the stated formula is the local linear approximation at 1 l l 4x a rvz A r x I y 7 h 2X v z t 2 y Based on Exercise 42 what would you conjecture is the lo cal linear approximation to r V J at l l l Verify your conjecture by nding this local linear approximation land l 48 Suppose that a function ftxy3 is d39 erentiab I the point 0211 2 and LLL y 2 x 2y 3g4 is the local linear approximation to f at 0 l23 w Find f0 l 2 3 0 Ir 2 filth l 2 am M0 12 49952 A function f S given along with a local linear approx imation L to f at a point P Use the information given m determine point P fXi39x2 2 AUXMl quot2 r ftx y x2y Lx quot39 56 The legs of a right triangle are measured to be 3 cm angle cm with a maximum error of005 cm in each measurement Use differentials to approximate the maximum possible er ror in the calculated value of a the hypotenuse and b the area of the triangle The period T ofa simple pendulum with small oscillations is calculated from the formula T 2n Lg where L is the length of the pendulum and g is the acceleration dim to gravtty Suppose that measured values of L and g ha errors of at most 05 and 01 respectively Use differ entials to approximate the maximum percentage errot in calculated value of T According to the ideal gas law the pressure temperatur h and volume tilquot a confined gas are related by P kTV where k is a constant Use differentials to approximate mp 2 at the pmni M y 39 zl fun v m 39 inn m my r 68 Writing 1 wear tion 0395 7 i V UlCK EHECK ANSWERS 714 J r Vl 39v n l L 7 3 i 1 la 7 Emmy my 71 b 3 fix yo 39r f x0 Mm VS v s w 7 3 THE CHADN RULE i 774 QHMN RULES FQR D ERW l VEE If y is a ClifferentiablE function of x and x is a differentiable function of It then the chain rule tor functions of one variable states th t under composition v becomes a differentiable function lift with We will HOW dentc a vm saicm of the chain in A sume that flit 32 lg ii function oi 39 functinns off a Single variabls I my Answers to OddNumbered Exemises Eli iii Sat Page 936 1 39x2y2 169v c d y 1 mg b 5 a 4cogt7 b 2cos7 7 azax 4azay 112 249 11112 ill Q fx m ha I as its graph f has I as39 sgruph nd f its graph Responses to True questions may be abridged U have spake 13 True on y 2 fx 2 c is a constant function of r 11 True 2 must be a linear function 0er and v 17 8xy3e 2quot312x2y2e 2v 13954 13y35 x 3x2 lnl xy 4 T 1 7 1393 quot 7 1 yx2 yz 1 x2 y2 7 I 12 211 32x2V5x2 73x5y 7r3y392 12 3x2 7134 5y 7x3y392 H i V lZ 42 2 V A 2 39 39 v 3 tan yz X2 yz x2 I y 7 y2 5602x012 Ianx73 y1anxy21anx 11 6 21 JL 1J Bf a 201413 y h4r2y3z3 x c 3J2y422 22 d12y4z3 e 123 1 1438 7 x zyl xzycos ztanz PK y2z3l xzy4zquot 2Xvz3 x2y4396 3xvzzzI A39Zy4z6 61 yzez cosxz e sinx yeWsinuZ X c0lt39z 4H xAx2 y2 22 v1r2 2 2 z1r2 y2 M ae b 2e c e 41 h 71 j 3941 f F I x C 739 l 3v 21 21 3 h 0110048 339 aLeet l vlr39 l b0101554 05 11111 12 44 11 F1 101 8 013 0 b r c 11 d gt sz trciriii SS2 115


Buy Material

Are you sure you want to buy this material for

25 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

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."

Jennifer McGill UCSF Med School

"Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

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."


"Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

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.