sol#7 - MATH 171-10c Assignment 7 Guidelines e = ‘ Begin...

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Unformatted text preview: MATH 171-10c, Assignment 7 Guidelines - e = ‘ Begin by answering the questiOns in the space provided; you may write on both sides of the paper. Additional sheets may be attached if necessaryx’ Staple all sheets together before submission. Igut doWn the names'of all group members in the top right corner. Write, neatly and legibly; untidy presentation may lead to appropriate penalization. 3'? Duéé Friday, March 12th(by;;5 pm): 1. (15 marks) 'fhere are two tangents to theellipse 31:2 + 16312 = 16 which pass through the point (4, —1). Determine the co—ordinates of their points of tangency on the curve. Show all yoursteps,_an_d explain (your reasoning clearly. Unjustified answers will receive no credit, even if they happen to be correct. 9' 2. (20 marks) Let C be the parametrig_,,eurve given by the vector equation r(t) ; (Rt 4 1),‘sin(27rt)) 0 5i 5 1. (i) ’Co'i'npute r’ft), 0 S t S 1,. , .. . _ (ii) Show that C is smooth (namely that r’ (t) gé 0 fer every 0 St S 1). (iii) Find, if any, the points on C where the tangent (to C) is horizontal. ‘ __ ._:_....,~v—————.——-——-r—r (iv) Determine the slope of the tangent to C’ at the point (é, if). ~—~WW~:--1 .. ; .agswwa...ww-w“ma-exuwmwkmm...;.mm--.~.fl..m..,.‘,.r~..,~_~,,..m-z - «WW- fem“. M "8 ' ' Wilt?“ « mm: a». ‘ Mam—.45.... A ._,. lLM .....-..._...~....c: i“ .. t .. . :_ 7 . ”away N. . 9 Let C‘m‘tol M r 1m“ ° :f”3““‘35‘ 3 MW - ‘5 9 I WWWMWW.W’MWWMMAxm~ . . I > 0/ - 31° New: 79+c) Bet—«use Z. ‘=‘- o_ ‘ ~= '1 - 5—. “it Sue/la a" 9;“b an" ”i“ 3 an a $9,‘!o) ‘5‘, We. brat. _ Y J, ' - I. 0.. .. mus? kc. \lt‘th‘vkl 6'“ ” ‘ .. ML '. Y m m. at. um] M—M—M - --~*,““'”‘“““;W” “ emery M Ns.._w....,-........wmw E1“ a; hat: ‘I- \(o . ' - 1' ' a. __ 7. r$¥°K +l9‘lo‘f: 3y°+ll°7° ‘ ”D =» t L we. ‘1 - ‘ 9 ‘I o ~ WWWWMWMWWWMW. {an .447. 5 '9 ‘7' WE) I‘kcs 215nm (De-55¢: WV°*3“‘ (Q‘V‘stg E a“ 1 — IV 1 * ‘Ch 3‘10 1* “-1 - . I 051: Wis \Ksb 3,1“ «A» 3 use b w 1* 7. V 7' 'L. In. (ii-Va) +370 : 3 2. ~ g = “-8 > 3 "=5 n= —'2.:\.‘\( 3'2. 3) «Yol‘i'lVo ‘7’ 2 O > Y 4+ - n We COTVQVS€GW Atwnélkgl 3$¢ : if (l+\£0) = 0 L9 (W51. *) ' a PI (Q‘ <““; “EC/“(KHz oak“. New. chow. m'ct) = 2b“ 7, 1 $9: I; 7, ask u. ‘Hnws 1'(t~) 2}. <3 .(iov a“: SmoeC’n. mm 3‘0») = o ) 0 ~ QE-k -.-. “4 4W ,1? ) fig, ~55¥ .kal W u-Ix 2. ' ‘ '1, abs‘urvcé. «Lavinia-w) 11(V4)” +- 0 ML ‘L'(3£q.) “f '3' ka‘; a4; “k: .as‘auc. is}; ll < 9,.553 -. . hm - ~ ...
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