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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.
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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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 Spring '07
 Sadler

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