3rd - 3.8 INE’I‘IRSE TRIGIJ‘NUMI'I'I'RIE...

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Unformatted text preview: 3.8 INE’I‘IRSE TRIGIJ‘NUMI'I'I'RIE FUNC'I‘IUNS rr Err 11' 3. {a} E {b} g ('3) 3 21. csc[scc_] 2] —cos (tan—1 (—\/§)) 2 csc (cos—1 — cos (— = csc —cos (— = 723 — = % d _ ' \- d \- 25. sec [tan—1 1— USE—1]]: sec (g — sin—1 2 sec [g — 2 sec = —«v 2 .v—., 2 .I' o . 40. (1- : 560—] ‘ x' ' 4 indicates the diagram I +4 2% sin (sec—1 : sin (1- : . _ x"— I'— 51. 3231:1163 : fl—¥%—JE—. = Han-1 (a T2. [at] y = D (b) 3’ = W [c] None, since ice-FIX = —] +1}: ;’ D. 3.9 RI~II.A'I"EI} RA TIES _ £2_ '3_'3 3— 3_ 3_3 E—fi d_’-_fi dV_flE 3 (a) 5—1”): 3' z 25—}: V 2 225m -xdl 4:“ _Id[ 2} E: x g_ V 92_ Z d_1 dt xxfllyerzfldt xxirY-zlz: dt wimp”: d1 - d_x_ $__V_E}1_+$ fb}F1'01]1palt(a}w1th dt —0 => at — dt dt - E_ _q :11 q.de qdz. ELK Edv zd2._ fc‘} Fl'Ol]1pfl11(El}Wlth dt — 0 => (1— .9: dt -3 ch .1 dt 2% at x D 11. Given % = —2cmfsec, 11—? = 2cm1‘5ec, ii = 12 cm and w = 5 cm. (a) A = {"w => % :1: 11—1: — w fi => % = 12(21— 5(—2) = 14cm315ec, increasing (b) P = 21: — 2w 3 5—“: = 2 fi — 2 cg—‘f = 21—21 — 2(2) 2 0cmf5ec,constant _ I 3 .—.«3_ 3 .3113 dD_] 2 .3-11'3 q dw 5.02 dD_WEi~*-1d—i _ 151121 111211—21 _ _ fl - _ m— _ 13 cmfsec, decreasmg 27. Let P01, y) represent a point on the curve 3* = x3 and F) the angle of inclination of a line containing P and the -- _): _J(3_ 3 d3 dx d19_ 3 dx -- d3— ougln. Consequently, tanfi _ x 2:» tan 9— —x _ x 2:» sec 9 —d[ _ —dt 2:» —d[ _cos 9 —dt. Since d1 _ 10 mfsec 2 _ x3 _ 3'—' _ 1 , d8 _ and cos fi|x=3 — Yin! — 92mm — 10,we have dl F3 — lradfsec. 3.11] LINICARIZA'HUN AND lHl-"l-"ICRICN'TIALS 2. 100: watt): 1:13—91”2 :» 1’01): (. 1 j (x3 — 91‘]"3(2x1 = :1» L00 2 01—4101 — 41— 0—4) = —4 >4 Z—f—étx—‘H—fi 2:» th):—%x—%at 9.1:(20—2113 4x 3 FOO—411 4 L(x)—f'( l)(x I) f(1)—0(x l) (5) L(x)— Satx— l 14. fix) 2 sin—1.11 => £01.11]: :1» L131]: 11:01— £01011}; — 01: x 25. y = sin [SM/E] = sin [511]”) => dy = [:cos[51i“3]] 21—133] dx => dy = (Ix \- 31. yze‘v’qzbciy: ‘11- 42. ft’x‘12114, 101: ],dx=fl.l 2:} f’t’flzxix‘i {a} fifzfilm—(ix)—ftm:i=f{l.l)—fi[l}=.4154] (b1 df = f’tmdx = 411131.11: .4 0:1 |m—c1f|=|.4041—.4|=.0041 46. V2213 :2 dvz'jxfidx 200—51e-1 4m 53. ¥ X 100% :5 % X 100% 2 [WWW dx. As saleschange from x = 145 to x = 150,131: 2 dx = 5 and _. I AV ggo_fl 44540-0 _ _ I % X 100% m ngmumfimm [5) >< 100% _ 2.2%. ...
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3rd - 3.8 INE’I‘IRSE TRIGIJ‘NUMI'I'I'RIE...

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