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Unformatted text preview: MATH 17110c, 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...www“maexuwmwkmm...;.mm.~.ﬂ..m..,.‘,.r~..,~_~,,..mz  «WW fem“. M "8 ' ' Wilt?“ « mm: a». ‘ Mam—.45.... A ._,. lLM ........_...~....c: i“ .. t .. . :_ 7 . ”away N. .
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 Spring '08
 STILLER
 Math

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