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MATH_200_spring_08_exam_2_with_solutions

# MATH_200_spring_08_exam_2_with_solutions - Exam One MATH...

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Unformatted text preview: Exam One MATH 200 Spring, 2008 Name 60 l/U'TMQ Mg?” Section 00 Show all your work on the exam paper, legibly and in detail, to receive full credit. N0 Calculators. NOTE: Page 4 just has pictures; there are no points for that page. Pg 1 (20 pts) Pg 2 (25 pts) Pg 3 (20 pts) Pg 5 (10 pts) Pg 6 (25 pts) Pg 7 (5 pts) Total (105 pts) 1a)(7 pts.) Find a vector in the direction of v = 2i + l j - 2k that has length l. ANS “(c-roe L L F IMO I new 83 ii \I 3 Z A 1 + Z : i ’ n-g Le—‘nwr'q BCCOME'S Z i L L 3 [ ) l) 3 A ll \l ll 3 UAI‘T vezﬂ‘oa 1b)(7 pts.) Find a vector which points in the opposite direction of v = 2i + l j - 2k which has length equal to 5. A (L; —" ls A L)ng Vane Polmdé V : aJ a") J to “We DIEGO-no.0 0F V) A \ -V Pawns m OPPDSH?‘ metre-mu] ~59 HA5 tmém S“) so lc)(6 pts.) Find the vector component of v along b. v:i+j+k,b:i-j+k : <Vjé>b 45L) (51» = «1661+ 1‘ =3) v-L, i H H443 +l~l Pagel V : 2a)(15 pts.) Show that lines L1 and L2 intersect and ﬁnd their point of intersection. ®Z¥£ L :x=2——l,y=2+3l,z=3+t “FED TD 1 L2:x=5——s,y=lS+4s,z=lO+2s \$5.,ng (9 2+5é 2b)(6 pts.) Find a vector perpendicular to the plane containing lines L1 and L2. (Same lines as in part (a)). lecc’c’rlold L/ * (I) 3d f) Dizezv'zm 62,) (O 96/ 2,) 0L \/ ‘ x . 3 I i (l 1 l 13/ [I \l (L 2 (I 2‘ AL) [2. +l1 [q l 25 l A A f 4 L 7" 'Q(—l—\+ TC 2 [274le 2c)(4 pts.) Find the equation of the plane containing lines L1 and L2 (Same lines as in part (21)) FLARE Mo‘o’l‘ HFWE (Wepgqmcuwa) DIQEWMAI (Zn’lJIB AND Cam/ml 0H€ F 776 Pﬁ/ma at: Poss/slams: On) T746 LIA/gs [,1 0A (,2- 3a)(5 pts.) What is the shape ofthe graph of r(l) : 2cos( l)i — 3 sin(l)° X’Zléos‘é/ 32/35/06 (:XZY +L_3~.>L=. C0814 +5201 :5]. KL ,5 79,4 (,JLL/xaft‘ TQgAJSL/JTEA ,_ vi; / 4+4 1 2.— Cb ._ /\3 X.‘ 3b)(15 pts.) Evaluate the indeﬁnite integral. j (sin(l)i + e’j)dt SGML) 9,6 50% =— [—6054 +~Cl) 891-ng / ’9 94) + c; 4&3]ng Vmé— = C— Coy/J [ZJNOTC/l) Page 3 Page 4 Match the following equations with the graphs ON THE PREVIOUS PAGE. If there is no match, write "NO MATCH". (1 point each). If you use a letter from the preVious page more than once, they both are counted wrong. M M a M 2 2 2 (5i) x__Z_+y_:0 ; N M 9 16 4 x2 Z2 y2 D 511 —-————l ( ) 4 16 2 ﬂ 2 2 2 (5iii) x__Z_+y—_1 l5 ( OQ‘ MM) Q 9 16 4 2 2 (5iV) 27—y?+x=0 I A 2 2 2 (5V) x__y_+Z_:—1 ; 4 3 2 2 2 2 (SW) x—+y__Z_:_1 . C (5Vii) iii: J M) 9162 (5Viii) x—2+y_2+i:1 ; E [0% (\) M)» a? 9 16 4 (51X)9 16 4—0‘ B fa Tm: gLuPSobe DID NOT 5 so err/er Cl—(OlCé was Piccﬁ/Wéﬂ CBW T00 Chis cor/g org g mug/‘5 Page 5 6a)(15 pts.) Find the equation of the tangent vector (velocity) for the curve r(l): r(t) : 1n(l)i + e’j + Z3k; Hm = +91? + 8‘3 +3.62 77414115 ﬂu, 0g AJAX/TEA! 6b)(10 pts.) Find the parametric equation of the line tangent to the graph of r(l) at the point wherel= l. A A r(Z):ln(l)i++l3k;l0:2 [n[43H—eé\\ +1.43 1.”. r6% 2 (mm) 62)?) Hm = +71? + em +332 / IA 2A A r (A 21—14—53 0 +lzb CA; {ﬁg URITTEN (mm +—%: 9 “462) 8+ mg} 017461 LJH Hrs) “(‘00 ‘. J Page 6 14) CL 7)(5 pts.) EXTRA CREDIT: Find the tensions in the cables shown in the accompanying ﬁgure if the block is in static equilibrium: {A Tumé [S MDKE 0/ L THAA OHFue'ar T° Do THlS [RO‘BW' Hmets 6/46! A K G— s A ’ » _ __ ~_ (4' : (Q05 (“50%) SM -— ( L) A) _ SM [tea—(90°) ML ’ (Cos (WonBJ C 3 2 < A; —q > L i“ / a —'> - o 2. o l'ul +mL'uL: —672”°°k’8 () a) V3 \ (P) “(3 ~ (5 2.156) ‘7) *1} “"ml 1 J 3’ ) Liv—L2“ so Mfg/Y” I _ (—2: 2 f‘ _E 5 a 25?) ’TW “imb ‘Z’n’ “fr—00’ A”; ‘ﬁ— : LOO ’Zmizz’oo W L ...
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MATH_200_spring_08_exam_2_with_solutions - Exam One MATH...

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