Quis 3 Solutions

# Quis 3 Solutions - APMA 212 uiz#3 Februa 7 2008 Name SW...

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Unformatted text preview: APMA 212 uiz #3 Februa 7 2008 Name: SW Write and sign the pledge. 1. (2 pts) Describe and sketch the space curve deﬁned by 17(1) 2 (3,3 cost,3 sin I). ' _ L 2 Z 3‘36” ’3‘ 3/4”“ -> 9+5 =€mLt+7w f =3 Cot/WC, ,m 7ft; W c/‘lcum 9f CLO/(«MM W I“; Zvﬂlm‘gecphm 2. For the space curve 17(1) 2 <§t3,tz,2t> (a) (2 pts) Find the unit tangent vector, T0) . (b) (2 pts) Find the parametric equations for the tangent to this curve through the tip of 17(1). . we 24%th (52,2) «mafafrzm MA H 33m’(t)c<!,2,2> .9. Eﬁnsof/tantjend’aélhcw: ‘xgé it) gas/+21; ﬁ'ﬁz'fzt‘ (c) (2 pts) Find the arc length for 0 S t S 1. I.” l 2, , 3 I, Ago I/» (ganja (t +ZJaLt—c[%+2t]0——é+2 .23.. m) x F"(t)‘ A0 __,, W w<t)=< 215,2,» —> m (I>=<2,z,o>, ‘X(I)‘=\/l+%+¢ (d) (2 pts) Find the curvature, K, at t = 1, using the formula: 1((1) = ﬁZUxX/(l): T T % :3 I Z 2 w<~4ﬂl~2> z 2. o Iﬁ’(t)x/'Tf’(l)]=‘f!b+lé+q=‘/3_é=9 . (a 2 ../C-_: \$ ._... (3)3 6; ...
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