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chapter 2 14 - 78 291im< 1 1>—lim1_vl t...

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Unformatted text preview: 78 291im< 1 1>—lim1_vl+t 11m————(1_11+t)(1+”1+t) I'm ‘t . —— — ———— :1 Ho t\/1+t t Hon/1+2: Ho tx/t+1(1+\/1+t) t—>0t\/l+t(1+\/1+t) lim _1 —__L_—__l t—>0\/1+t( +\/1+t) \/1+0(1+\/1+0) 2 . «5—222 . 730—953”) fi(1—\/5)(1+\/55+m) 30. 11:11} W : $1311 ——1:\/—T_ : $131311 ———1T\/_E_— [dnfterence of cubes] :1im[\/E(1+\/E+$)]:liml[1(1+1+1)]=3 CHAPTER 2 UMITS AND DERIVATIVES a:—»1 Another method: We “add and subtract" 1 in the numerator. and then split up the fraction: — 2 — 1 '+ 1 — 2 _ limfi—QL :1im(—‘/E__)—(—m—) : hm _1+(L_M 2—»1 1—\/:E w—rl 1*fi $—>1 l—fi . (1—fi)(1+\/E)(1+37) _ 1 1 ’ 1 1 i 1 1 i 1 — 31. (a) 1.5 (b) —0.001 71 1 —0.00001 -— 1.000001 70.5 0.000001 lim —‘”——— ~ g 0.00001 513-0 1/ 7 1 + 330 1 0.0001 0.001 . . 2 The 11m1t appears to be 3. 1. m \/1+313“—1) 1.111 $(v1+31:+1) im a:(\/1+3$+ - — 1 : _____——— (C)11:*%<V1+3x~1 x/1+3a:——1 z—vO (1+3m)—1 1-»0 3$ : lim (x/1+3$+1) l 3 l 3 z—>O [ /lim(1 —' 3m)+1im 1] m->0 $—’0 1H0 —311mm+1> 0.6661663 0.6666167 0.6666617 0.6666662 0.6666672 0.6666717 0.6667167 0.6671663 1) [Limit Law 3] [1 and 11] [1, 3, and 7] [7 and 8] ...
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