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chapter 2 42

# chapter 2 42 - 106 El CHAPTERZ LlMlTS AND DERIVATIVES(c lim...

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Unformatted text preview: 106 El CHAPTERZ LlMlTS AND DERIVATIVES (c) lim 4f(1:)_ lim (x/3mQ+8:E—l—6e\/3.7:2+3m+1)(\/3a:2+8m+6+¢3m2+3m+1) 1*00 r—“XJ 3\$2+8m+6+ 3m2+3\$+1 lim (3:162 +83: +6) — (3x2 +337 +1) 98-00 V3332+8x+6+v3m2 +3m+1 : lim (5x+5)(1/\$) H» («w + 8x + 6 + \/3\$2 + 3:5 + 1 ) (1/95) . 5 +5 : 11m ﬂ” — 5 z 3— : 5V3 % 1.443376 z~m 3+Ww+Wﬁ+wB+3ﬂ+lm2 v§+¢§ 2 3 6 . . 1 37. 11m {c — hm ——1— — 1. so y — 1 is a horizontal 12 m~toom+4 maioo1+4/\$ _ 1+0 . 2r . a: asymptote. hm :ooand 11m : —oo.sow: *4is z—>74— (E + 4 \$——>74+ as + 4 a vertical asymptote. The graph conﬁrms these calculations. 38. Sincem271—>0asx—>:t1andy<0for—1<1r<1andy>0for 2 2 4 4 ac<¥1andac>1.wehavelim a: + :—00. lim :1: + :00. mal’ 1132 — 1 z—>1+ 5132 ' 1 2 2 4 lim m + :oo.and lim \$ +4 zeoo.soa::1andac: ~1 z—>71’ \$2 — 1 Qua—1+ 1'2 _ 1 are vertical asymptotes. Also 2 2 1 4 lim :3 +4 : hm le—i—E :1.soy:1isa zH::oo 172 i 1 m—t::oo 1 # 1/\$2 1 - 0 horizontal asymptote. The graph conﬁrms these calculations. IE3 :8 3 . ‘ ————- = 1' ——-—’—'—— : i . th ' 9 121100 \$2+3\$110 x—1>I:I:loo 1+(3/\$)_(10/\$2) 00 SO ere lS no horizontal asymptote. lim (ms—— : lim ——’x:——— : 00. since ac-»2+ \$2 + 31' — 10 112+ (w + 5)(a: — 2) :33 . . . :63 m > 0 form > 2. Similarly. @1351— m : #00. 3 3 1“.“ 97%;?) Z #00 3““ 1“? m I 0°— (I: 2 2 and a: : —5 are vertical asymptotes. The graph conﬁrms these calculations. #14 ! 6 712 ‘Il4 10 ...
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