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Test 2 solutions - M408D Spring 2010 Test 2 K63 EID Name...

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Unformatted text preview: M408D Spring 2010 Test 2 K63 EID Name — Printed Circle Discussion Time: 8:30 1:00 4:00 5:00 No calculators, cell phones, etc. allowed. Circle your answers. Each problem is worth 10 points. Choose any 9 problems. Problem not to grade: . Show your work. 1. Write parametric equations for the curve 4m2 + 33/2 = 12. ‘L 7.. 3»: é’fl" 2. Sketch the curve r = 1 — 2sin6, 0 S «9 S 27r on the given axes. 3. Find the slope of the tangent line to the curve r = 1 + c080 at 0 = 7r / 2. X: r‘(ox&; (/7‘013) (arfi: (0§@ ‘f'KoILél X/(§>: —-;m& + 2(05§[-—JM§) X,( “71> '2 ”l ‘0 ’ Hm é‘ Jm§ + (osfix/AEL {fl/(&’> C‘ACfi” ’Jmi’fi’ +(057'fl- 4 Express as a definite integral but do not evaluate the length of the curve C given byxzt,y=ln(t)1<t<3 4V): gm X6 x6763: ) (g (6): 2‘ 5. Let E : (11, —7, —11) and 5: (2, —-3, —4). Find vectors 11’ and 1730 that (i = 17,417, 17 is parallel to I; and 17’ is perpendicular to 5. ‘ .7 v __5 _> a.» E7 v) ”.2 —|— (— 7)/’3)+ MI. 7) A /— A \ __ /______—_——-———- : PU 0* —- ”:3: A +9 Jr M M P lo Ht // L7 6. Find the equation of the line E through the point (—1, 2, 3) which is perpendicular to both vectors <——1,0,2) and (2,4,1). ~> <K {32)3> + ‘LZZ 69 /> —/> L D ,5, Elm ; v7 7. Find the nearest point on 7"(t) : (1 — t, 1+ 2t, 4 ~— 3t) to (13,11,—12). [/33“)‘12) 53(6) 2 ()3)“)_.,2> __</__t) )fzf) 7'3‘6> <12+f) /0 -2 2f) a/g +3f> ‘7 Wm 5819 J 0Q=<-I)2,-3> A m4 :_ ~12 fie +20“5’6 +98%“ —,—_ Et—Mf =0 i? 16::‘1 fit > 9. Find the cos of the angle of intersection of the planes 2:17 — y —- z = 4 and3x+4y+52=7. 4 7]" 7-? ()1; fa ”MS/Q Mg”) Dffi‘ /Z M ——7 /> 2 C0€&; //‘/l'fl/2” /,_ 3 ”A “VE‘B’OD M?» II min L : E 7“ AME “9 10. Find the point of intersection of F(t) = (2 — 5t, 1 +375, 4+t) and 2m +y+3z = 33. ,2 (2—Sf3+(/+3£)+ 3[7+L/;>:33 «zo 7? Ht 3?? +/z+375:?3 4 [172,4 : 33’/7—:/{ ...
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