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# midterm - Evil—DTERM EXAM FDR MATHlDﬂ-LZ FALL EGG<1...

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Unformatted text preview: Evil—DTERM EXAM FDR MATHlDﬂ-LZ, FALL EGG-<1 Instructigns: 1. Write down course ggde [matthﬂ-LZ}, name, and studth ID gynhg on the carer of answer book. 2. 1|Write your answers on the EIGHT—HAND page. Use the left—hand page for rough work only. Any work on left-hand page will NOT be marked. 3. Begin each question on a NEW1 RIGHT—HAND page. 1Write down the corresponding question number at the top of each solution. 4. Questions should he answered according to the ORDER the}r appear in this question sheet. If you skip one question: leave one righthand page for the skipped question because you may want to go back to that question later. 5, You have totallyr 1D RIGHT-HAND pages for 53 questions. QUESTIONS: 1. Let 1ft} = ti+t3j +t3k. Find the value of re) - {r’it} x run at t = 1. (10 points} 2. Find the arc length parametrization of the line 3:144, p=3-2t1s=4+2t that has the same direction as the giVEn line and has reference point {1,3,4}. [1D points] 3. Sketch the letrel'enrve s = I: for the speciﬁed valueo of it. The function is a = 5:2 + 3; anti 1% = —1,l'.l+ 1. [:11] points) 4. Find the limits of _sfs_ Ens + y: as (my) —r (U, [3] along [a] y = L [b] y = \$2, and {o} y = :3. {1D points] 5. Salem-ate 63/55: and as} 613; using implicit diﬁerentiation for 311(232 +y — 2:3) = m. Leave your answers in terms of 2:, y, and a. [ll] points} 6. Find the local linear approximation L' to‘ the function I W at point PM, 3). Use L to anpatentiinatelj.r evaluate ffs, y} at {3(332, 3H1). [ll] points} fix? y} = T. GiVen that foze,yﬂ} = i —- 2j and Duf{EUT‘yﬂ} = —2, ﬁnd the two solutions for the unit veotor u. [1!] points} 8. Show that the equation of the plane that is tangent to the paraboloid I: yﬂ s=-G—2+§ at (on, ya, 3g} can he mitten in the form 2553a 233's + 24-33: “'2 £12 . (1D points) 9. (linen a point P{mn,yn,sul and a plane as: + by + es + d = [1, where P is out of the plane {Era + Eryn + ea; + Li # El} and a, t, e are all nonzero constants. Q{n,o,w) is a point in. the plane that is closest to P. Show that the angle heWﬂn the two vectors 1% and (n, h, e} is I] or fr. {2!} points} ———______________________ Wight??? ,; 200‘? fwd; Wax-:94, /00-—L2 —3- —} t t2 3:3 3- fvr'ﬂ- (Fr-H Xfur‘ﬁJ): .-" 2.15 3133/ rho-2163 c? 2 6‘75 At 75:1,. he efmzs n. 2,. 2n Sfity sz=Hsﬂ M7320 =ff JUL) +0”) Hz)?— 49'? —/ r953 2522 _ {PE/3 FHSMM mfg Fiﬁ) 21(5) ZXE'ZAI’SJJ— {+35 ; )lfs-)=.3-——-—-g erj=7t+§5 lewd. Enrt’es k}: Z2 "ﬁg ﬂ=k"ﬁcl J47?“ ’16:“! 0 +.I' 96% j:;[: AA“. 2 g 2 a??? \$2: ’ 96 FHA: 2. 23-50 2:39;; 95790 é fw=% : -"-_-‘—————x L— f" (ﬂyvé‘z ’ at“ )‘ f; 09—1“ M054 ’ at”? :5? f : — + —— ._ irzcajj= ihiijg/HW ‘H +{ £72013) 5 32.5- 393 ‘4) “T—zf (3 93' "-3) o : .2023: 7 {Dacmi’i’f was.) m,»- <; —.2>= za- .2241:— (LL, 7* I4: =:’ Plat/f 2%.! = “21‘2“3 :‘n'fo Miz‘fﬂzz 21" \$774.1. 131%.: +3=o , (Ema—3)(2,ga—;)=0 352:? ; %J=_% %:_5?+g: M32! J' Mfr—<0 i=3 *2? _?_z_:2% \$1-32 9% of: J ay"b* TWE'YME fKam , Z=Ka+2§fX“xo)+%{/— ca.) _ x5 yf Ema aﬂ-g—Ll—wkba , 19M awn—2?}? 14—” 2 9* g (2 (“z/c 25a) Trv—yﬂ) +(En/ .20) 9—%¢=o —+ 2(% mj+2(W—z,} 231—0 9M 2 -9__ :g -——?-- 2rL/Hng-s- ZE'M/h-J'Zu) 1‘1 he 91/ 91/ mm+év+cw+d29 .. %£=—% %ﬂ=—i ML: L M: i I "—‘f ‘3 %_%ﬂ (,1, ’ V_); b .. P152 =k<agégc>. <14— ?Q, l/- )4}, W .220): kx/ﬁulu 3) ,, his @‘ﬂaJ’LZ-ﬁf‘o PM or Mﬁfmééé, ﬁﬁé— :2: a WETFMSL ...
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