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chapter 2 39

# chapter 2 39 - SECTION 2.6 LIMiTS ATtNFlNlTY; El 103 1 3\$...

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Unformatted text preview: SECTION 2.6 LIMiTS ATtNFlNlTY;HORIZONTALASYMPTOTES El 103 . . 1 . 3\$+5 , (3:1:+5)/ac 3+5/mﬁm13203+5m13‘20\$_3+5(0) 3 14. 11m 2 11m _ 11m _ 1 _1 40 m zﬁool_4 z—‘oo (at—4V1” ac—‘Do1_4/m 1iml—4lim— ‘ () :B-—>oo (tr—’00 23 . 2 _ _1 15 l‘ 1— a: — 2:2 _ lim (1 — :3 v I132)/£E2 _ whniooU/x 1/9: ) I w—lpr—noo 2372 — 7 — x—v—oo (211:2 —— 7)/.’,E2 — 11131 (2 — 7/132) _ mﬁlltou/xg) _ 9.5131000”) ‘ \$531001 _ 0 — 0 — 1 _ _l _ hm 2 — 7 hm (1/132) ” 2 — 7(0) 2 1' 2 2,3 2hm 1 2 —lim3 16 Iim 2_3y2 _ lim (2_3y2)/y2 _ yggj /y )2 FR} /31) yam _ 2(0) _3 : _§ I y—>oo 5y2+4y i y—ioo (5342 —ir4y)/y2 lim (5+4/y) lim 5+4 lim (1/y) 5+4(0) 5 y—roo y—>oo y—>oo 17. Divide both the numerator and denominator by :53 (the highest power of m that occurs in the denominator) 3 5 . \$3+5\$ . 9:3 . 1+; mggo( +\$2) 11m ‘211111 #2 11m %: 190021133—11724'4 z—wOZx —a: +4 Iﬂoo271+i 1. 2 1 4 T a: ms .133. ‘ g + E . . 1 _ 3334.533”: 1+5(0) ﬂ 1 hm 2— hm 1+4 hm is 2‘0””) 2 race z—roo 1; spam £17 2 2 3 2 t 2 t 3 18. hm L— hm ( + )/ — hm ”HQ/t 2 0+0 ‘0 t>oot3 : t2 1 z > oo(t3 : t2 1)/t3 ta—oo1+1/t—1/t3 1+0—0 19. First. multiply the factors in the denominator. Then divide both the numerator and denominator by 1L4. 4u4 + 5 5 lim 41‘4” — hm 41‘4” — 1‘1 “4 4 r ‘AHu—‘l u oo (u2 2)(2u2 1) ‘1. we 2u4 5u2+2 13330 2u4_5u2+2 ‘13; 5 2 2 ~ — + _ U4 ”2 U4 Iim (4+ 3) - - 1 I We U4 _ .1320“ 5.1220174 4+5(0) hm <2_ 3+3) hm 275 hm i+2 hm i 2‘5(0)+2(0) u—roo U2 U4 uﬂoo u—voo 1L2 uaoo U4 4 _ 5 _ 2 20. hm L”: hm (“Ln/3” — hm 1+2” d 1+0 :1 I—‘m 9m2+1 1‘00 x/gm2—t—1/x/ac2 I—wo 9+1/a32 9+0 3 6h 6_ 3 limx/ 9305—1; :36 21. lim M : hm KM ( V = k - 3 : 6 z—roo m3 + 1 x—boo (\$3 + ”/5055 lim (1 +1/m3) [Since :6 Va: form > 0] m—>OO lim «9— 1/535 lim 9— lim (1/m5) z—wo mace lim 1+ 1im(1/:c3) ¥ 1 + 0 1‘—>oo z—boO =x/9—0=3 ...
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