MTH132-Test2-Sol - Page 1 2008—10—9 Name (Print...

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Unformatted text preview: Page 1 2008—10—9 Name (Print Clearly): Student Number: MTH132 Section 5 & 18, Test 2 Oct 10, 2008 Instructor: Dr. W. Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 50 minutes. 1 [5 pts each]. Find dy / dx of each of the following functions. Do Not Simplify . ; my ~ i i a wt» a mg i V1 1:53 I}; 1‘: fié’g‘m> £k1i«{}“)f:3 ” W "3 (b) y=<4x+3)“ l g; Xi}??? K“ fig ,, ~ ;’ , r a, L (c) y : (cscx + cot x)“1 ‘ P / rig . « t” \ j}! ::..,, m3 (5‘3" i” 1“” " i it»??? ‘1‘“ if all 3'; “(rim +~55tvP<J ~ 5,“ *éMde "“ Wax} (d) y = —1-sin_5 x —— ~x—coss x x 3 i s M, ) , my”; K m... Whv» '1 a; a: “X? “7m 7x r i w Page 2 M {Kins +3} ‘* f m “1..” way mm»... d 4W~VHW = 2x (use implicit differentiation) ‘ if}; . a”; 2 [5 pts each]. Let = 1 . 2x +1 (a) Find the den'vative using the definition. is: : its} fie} \ i, ; ~. g k j {A} w{,i,m, WWW—mtfm " x W A .m.’ M ma, J x M {'2 «842252 infigth (b) Find the derivative using differentiation rules. £2 4 W"; . < Em} g. ‘w> W! “a” {fit a 3 5‘ «mm. methm‘ 2008—109 » 5-5 . V dd; “‘3 a”: t , (7M 5 {32 «é a} 4? Y m , g, a“. ,{WW‘WV , ~ :5, Page 3 2008—10-9 ? l} 3 [10 pts]. Show that (17 1) lies on the curve x3323 + y2 = x + y . Then find an equation for the tangent line to the curve at this point. ain‘t. it «a; l ” ‘KK: m? ‘1: f t l ta m {it’wlgttwilgz t~§ M“? *5? t “ 4 [10 pts]. Water drains from a conical tank at the rate of “5mg / min . The tank stands point down and has a height 1 0m and a base radius of 4m . Suppose the water is 6m deep at this moment. (a) What is the relation between radius of the surface and the depth of the water? b “v a in 353,3” ~33“; jaw 52%” {as}; 3 WW”? 2 " i g f N173» no Em twp/3' m “ y ._ i 55;" , 3 if E9}! K “t Wig-{m ; “ailing é‘zkirjfsg’itfléj a; {Vii \f/ i a y p ‘4 .J i >’ iv; 14“? ‘ A 3"; M M W (b) What is the relation between the volume and depth of the water? ' , V -g " . M» W , 5/ E73; “3’1 x F w, ' w V. Q. _ j “W1 a I} (c) How fast is the water level dropping at this moment? 4’" "a I f If“? 51’ // t («£1 Wf’f’jg ~ V54“) ’7“ We x} / {ft/E’kesx f; 6:; m 343% nu ‘3 “" Ms J , ‘2 £715” g5 w lg e. a? "l gig C! E; Page 4 2008-10-9 5. [10 pts]. Letf(x) 2 \/1+ x + sinx— 0.5 iwi: k I a g m (a) Find the linearization of f (x) at x = 0 . ’ {WW 4, a n «x g~~ m i“ e) it; Mr; i~ 5%; at; t2» Es M l L} * J r it ‘4 ~ I ~ “ ’ 9 i In“: 2!; i", i f .. ‘““ mi e1?» r’ 1* x“ ,i i ‘3: {a} "e + a}? J i" E “"4“ K! ">3 t V 3‘ if M i J » if” [A is, 9 u i f‘ a a; f k H" We if ,a Lik) «. j») r“ j’gwixw 51‘; w 5‘ ,9 {113% (b) Estimate f (0. 1) using the result of (a). “ Xi m. w 3‘} w “2 <5“ .4 g {‘2. «w j" “£15315? w“ 3‘5 W3} J‘s ‘r’ m" ‘ w} 6. [4 pts bonus]. When a tanker collides with a boat, 100% m3 of oil is spilled in the ocean. The resulting oil slick forms a right circular cylinder on the surface of the water. If the thickness of the slick is decreasing at a rate of 0.001111 / sec , how fast is the radius increasing when the slick is 0.01m thick? 1 W i : a"); iri,£5£irlil’iw a "if « V3 5“ g. i B i 5" ":téfi L*§Iaii§‘ ‘ g&1~‘ (3" 3” i :3: “:9 i’x’wiiu cf R W % M (g 4‘ .u E} 4; N. L, J r" J a :3 g, a“ 2», 3;; i; f m a; iii: «:5 *3; « ...
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MTH132-Test2-Sol - Page 1 2008—10—9 Name (Print...

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