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Assignment #8

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School
University of Alberta**We aren't endorsed by this school
Course
MATH 100
Subject
Mathematics
Date
Dec 17, 2024
Pages
8
Uploaded by DukeEnergy9648
Onlne i ™ | N O 4, x (G- 1 - ten(o0)) [0 T | o 2 & 00 200 ol L Lo w» tim % (+4x? €200 x-z lim 212 0w (2 ! tim 212 424\ X700 (24| 24| -1 |- lim X700 Lo 24\ N~ @ lim sinh (4z¢) — sin (4x) ax? lm _3txt >00 ?x? 9+ 8 L Sx? 5% (34 24)(225) 220 om(xc®) 4 ! 4 (‘.mex— 4o tim Zex— 4 2250 3 220 3 4 4 (m Ge =4 (m 2 =4 x>0 322 250 322 - 6 eéz - geéz x20 6 x20 6 Lm 64e™_ 32 64 lim 2™ 32 x20 g - E X 3 x20 g - ? (@ Find Stant osymote eqin of Py =< X1t x| b= lm fxy-mxe 2200 8)8 N —|
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AL =l 2 IEAT l‘ - “ fand 4 x50 ____J:':‘ a;:nao =1 B4l 2200 [zA\ = lim x J;u? 2200 - Efl y= x+3 = [k Jx-fl = = lm x - = oo = lim x- il 311 xoo0 " fem (Gevre G lm x - 5 X200 (xPgxat+ X = bm 6x X200 (resx 1) 1) @ Given & cardboa®l box W Squote base and open p thatr has a volum of 92200 wm?® What s the latsest possible volume ? Sk = b% + 4l V= bZh h @b SA= b (b +4h) b2(577°° -b) —-byx'—_h K K V= %3c0b - % V's %0 - 24 0= 2%%0 - %bz -»bL=180 Viex = 256000 cm® ->h=40 ® A famer wonts © fence an orea of 315 mil m® in flectongulor Ffeld and then divide it in half wih ¢ ferce parallel ©one of the sides of rectongle What is the length of the Sicles of the fecangle ™ minimize the cost ? a A=37S = ab SA = 36+2 . B . s b= —; SA a + 2a
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0= -usc?+2 -2 =-02s a= 1S » 7500 m »>b=5 > 5000m Wy ’tTetf\ ® o) Euwalvae lim ?Zffif" o ~oo 9x -1 3x 2x+5 i (557) x2-00 lim xs-ao 637: [b\ (2z+5) —(n(2x~ l\] fi"."oo 3x[£n(2z+s) -m(zx—n] let x=-t lim -3¢ [Ln(—?tfs)-ln(—zc—l)] €>00 -3 lim n(-26+5) - tn (-2¢ 1) €200 t" — (p- 2 (-2) -3 lim —2¢45 -2t - €»00 PN 9 . ) o lm (£ _ L) 2 3 o0 (9:—5 2t (¢%) lim Gt+2 ~(4t-(0) o2 €22 (9¢-5)(2¢+1) % 2 —_— [¢2? G2-8t -5 () ez G?2-8t -5 3x 3x 2x+45 2xt5 . S . 2x+5 _ lim = _ >(c‘:m>oo Qx-l) ’g-’-m e (2x ') - eg
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zx C> Let () = ax , fna all csymwtc - foey .2 Slant asymmte M = ?:l;,_“_‘,"m Bow il b= lm - = i =) xaoowv MX = 2a00 tomx T P _ - 2 (2T v i T ) m-( z+0) o =0 — x00 7T ' R T 2 2 Stant Asymmvote |y = f-\_’C H.A . — gflo o = - No HA m x_ _ x>0 g - % L x = 'm0 2 = O (possible VA) x O U'H ! bm £ 08 lm X>0° ol O 20 U 1+x? ; x ; x LHL= bm o = - tm = - x20" tznx ~ x-0" wax L . X OoH (! ’(LA::‘)+ m—;‘-"ea — a0t 1— = 4 - Lmit exist-, no VA 1+x?
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Slant ksymote y=—2-2 V.A x =4 L.Max (2,3 a T.PL.0) Slant. Agymtore y=2 TP (10,1) (x-2)3 x? ) ey = @ o = &) Domain l)? = (—oo,o)U(O;N) b) Asqmbk: = No H.A 2 (x-2)2(x+4) o oot ’ ¢ 7 r L.Mn‘v\(?,@} be) = t ([o] 2e(x-2) I‘l
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(-2 = x° - 322+ 8x(a) - & lflflg division 2c -8 = x 2 - g2t x? x? ,xs,ézz + 12x ~8 > Slant asymmie = y° X-€ ~6x? +122¢- & +6x* 122 -8 ¢) Tncrease [Decrease Treeval (x-2)2(x+4) ity = pory > x220,2,-4 = I £0cy & increasing on (- 00,4YU (0, 00) -4 © 2 f6o) s decteasing om (-4, 0) A local wax / min (-4-9)° local waxot x = -4 , P()= (-a)? -85 &) (oncavily intecval ” 24(x - ey = ——(’;—2) > %-0,2 - - fty s concave down at (-00,2) o 2 fx) s concae up ot (2,00) P) Twfecton pornt (2-2 TPat x=2 , f2)- 7)320 ©) Suetch VA x=0
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Q00¢g = 2 = OG= 0% = oY pauud wd xo W X009 =0 X9y XS cpe WO @rg’ :i Sooz = V¢ X 02490 <D Wl = owef =v %‘:%‘q 0005-6. ob=9 Q008 = zu S 20 goog * 5 =0 o] =I£ ~ VO 220w P D L= + G- <= 1_:_p 02 +-2 " o - 05 ~ 00 - ~ “OZ (o i (S~ oz N>-2) = (s5-9) (- Wg/‘g P2 W -~ m = 2 z Va0 wud YY) w m’v )QOI (’0 Ob ey (se-'>-) xow'7 (92)91
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2p +0) _2 2%+ 9 YW +r-9-2890v - 200+ 00 = 2pr+01 o - 8579 =% 2o “ 2% -8 g v 22y 08 - '3 (20+2)- O 2+ 8 g (')('.} wea) 77 Y 2r+e 4 9! AV y‘z—m} vty <Py (' 20 +2 )é_:z a - ys-a/ll a3 Y] _2p+Z » Y- ¥s-o = QT;ZW « ,péy pS<Gas &y = (Y+3)0 =22 +9¢ «d '2 25y «4 2 S SN 25 -01= 9+ ; ; ZJ - '2 ’ ¢ jouy uw 12b @ 102G M R gMoys Moy cbvoyL 599225051 WP VD aw meG S) SOYO Tyl VMO wombs QW Lvag § WP * s20ad 7 aw s g wzrs-g wm y @
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