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# MultivariateCalculus MATH200

Drexel

GPA 3.63

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## 54

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## 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.

## Reviews for MultivariateCalculus

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Date Created: 09/23/15

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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 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