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Limits (Intuitive Approach) - 52 “1717.3 INTUITIUE...

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Unformatted text preview: 52.! “1717.3 .' INTUITIUE flPI’RDHC» SODE 777/1065 To NOTJCE , - Pu) =3 . HowEVER, wh‘EN X 13 CLOSE To (Bur ~01 500m. 10 ) 1 Fax) as mass T0 4. D - THE CLOSER 1 '5 TO I (BUT snu. ~01 sown. TD 1)) THE (31.0550? Pot) as To H, ' Put) em as more as cwse as you LIKE To I] JUST BY CHOOSWG at mass ENOUGH To 0301 ~01 EQUAL To ) )_ " THE leT as x APPRMCHES I 0F Ax) as ‘4. d H 1m Fun) :11 X-‘l 'q 0 GRHPH 0F y: FLX) 3 I 1 “14 ”-m—p .. wuwat‘ -<—~——~—~_...- ’ -g .5' u] -3 .3. .4 l ‘4 5' 6 ‘7 .g i .7, : .3 : .q ‘ ' FL-s) = 3 . wmsw x as CLosE To (BUT ~01 500m. 10) ~3’ Fox) .5 mass TD 3, - Fm) can: BE maps as CLOSE as you LIKE To 3 3y Chooswc x SUFFICIENTLY cLosE To (BUT NOT Baum. TD ) ~3. I I 'THE mm as x BPPRoncIrES -3 OF 9.x) :5 3 ' " hn PLX) =3. 36-5-3 .. Inn PM): FL—S) x-3-3 ’14 s i GRHPHDF a: Y: FL“) 3 . 1 i I " z t .. ... A..-_,_._. - _. ..._‘.h ,_,.._,___§ ’ : f a x -1, .5' .01 -3 .1 -1 | .2 -? 5' 6 -1 ; .UL i -3 i 2 ul’ e ‘ PM) :5 mar DEFINED, Bur NevERmELEss " Im ch) a .. x-w . R3) )5 ~01“ DEFINED AND “WE'RE IS NO NUMBER 771197 Fat) )5 CLOSE TO wh‘EN x IS CLOSE TO 3 0‘ I lm fix) 0058 N07 EXIST ' X-53 . 9L2) = I, BUT NEVERTHELESS THERE :5 mo (swans) nunssa mm- Pnc) :s CLOSE To «Win x IS cwss To .2 " hn Ex) 0053 10075me 3:41 ‘I [q a i i GRHPHDF si Y:FLX) 3 . E l I 3. w i t ” “”‘“' “ ““ “‘ *~~-—--~~: : s I -7 vb ~5 ~‘i -3 q, -l 1 2 3 n4 5- 4 amen/9L DEannoms : LET Pu) BE 9 chnom mm a. H mm NUDBER L war may on may ~01 as m we Donfiw 0F P ). wE say Trmr T__’_7_§ Lmn‘fis x APPRoBcHEsa. 9; Put) _I_§ L, comm-en) lm pcx) = L x-sa 9 u: FLx) can: BE new: BRBITfifiRJLy cLosE T0 L :31 CHooswa x SUFFICIENTL)’ CLOSE To ( BUT NOT Baum. To )0; IF mo sucu NUDBER 5x053, ’Tm-‘m we say m7 lm Pun was New extsr ( one )_ Y-DA To 651 Pu) THIS cLosE To L , choose at rms CLOSE r0 4 \J E a. t BUT mar EGUfiL To a. ) phat) l 1 a u a ; ‘ i i u a J I >7 il a I: u WE WILL $70177 CODPUTING EXfiDPLES NEXT 770E, BUT HERE fiRE A FEW "om/mus" exnnmss: l. lm 5x :15‘ LE): cnweannoemcwss x ~49 3 as you Laws 129 I5 BY 0100st x cuss ENOUGH To 3 ) l .L. .2, I" x“ DOES Nor 5x157 y x—v o I I II] 3. m 7 Does ~01 EXIST X“? O ..| A FEW DORE TYPES OF LInITS : GRHPH 0F y:pL¥) 3 a. ._.-. n4 a-‘b‘u'w— —~—~~-- -—~.«v~»~——...- ' ~‘7 “(a ~5 ~“I -3 -g -l «I .1 '3 up ONE-SIDED LH'HTS : FRon BELow: Im Fax) : .1 Y—vg“ Fnanflaové: 1m Pa; = I x-n.“ L Put) can: BE mans amssmnmy cwsE TD .2 By cumsuos x SUFFICIENTLY cwsa TO) M L51? my «I ) ( Fat) cram as nnoE ansmmmy CLOSE TD 1 By cnoosamc x suFFIcn-wny cwsE To, 5112 mean-'1? mm .1 ) l m pun) ooE-s ~01 EXIST 16—53- lm Pa) 0055 M27 5x151 x—>3* To DESCRIBE DORE EXPLDCITLY rIrE nfiNNER no wmcn THESE umrg FHIL TD EXIST we WILL wmrE Inn put) = °° Xas’ AM) ha fix) = "°° x—hs" more mm ms sour 0F mums Iffll’PENS AT 9 vsmlcm nsynPToTE . {q . GRBPH 07" Y : FD" 3 ' 3. [In pcx) xa-w L Put) can: as nine HRBITPHRILY CLOSE TO I [I —- sy CI-IoosWG Ix! SUFFICIENTLY L/M’GE wma x Necnnve ) NOTE 771297 77m wmcenss B Homzomml. AsynProTE HT ”from I, lm poo 0055 um 5x157. noiae expucmyl x—arco 1m Pox.) = °° x—»°° ...
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