Indeterminate Forms

# Indeterminate Forms - H L’Hémrm's RULE nEanL...

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Unformatted text preview: H L’Hémrm's RULE nEanL : zmosrsrs’mmms was : O I 2.“...3 4’ O ‘5" "‘7 9m) -+ a 39... PM) -+ 3°" co Ian """"' " EXTRﬁ woRK REQUIRED " To DETERUWE THE Lmrr. SonETmES THIS I. x ~4 .5 easy (5.0., “Lari 3-1- ) mm sonETmEs :13 NOT 5m X (56., lm x ' X~§0 THIS SECTION INTRODUCES 6 N51» vooL FDR Comm/MG SUCH 1.217275. 70 SEE wﬁERE IT Fonts FRon , 1mm ﬁBoUT THE FmLowuva SITUHTIOM I Fax) ~9 0 lm -—-) X-va. 3m '4 O was” Put) AND 30:) ARE DIFFERENTMBLE (MD WREFME CONTINUOUS .30 Pm) = Ian Fax) = 0 am: gm): ’m 50¢) = 0). x4”. ¥*"4 THEN I,” Put) - l’n P‘X)'Pl4) *4,“ got) you; gun-31a.) x a. 116......»— (PROVIDED Tvs DEmomanois .. ) lm w:— 13 ~01 ZERO ) X-M c movmeo F'cx) MD 5220 1m 3 (3‘ ) ARE nLSo caN‘rwuous 3 "ORE CHREFUL monsms snow TﬁﬁT Im £953 = 1m £99 Fog ESSENTIHLLY 01.1. or 71/5 vnmovs TYPES 0;“ 1.117175 we MW! + .- conPuvfo (x+a,x-=ra x—aa x—Ha, x—a-w ) PﬁowDEp C—-——— Pm °° rum lm --—~ IS OF TYPE 3- R g; I was :s ammo L'H5PI'ML‘9 302.5 : IF EIWER I Put) «Jr a I £29, "’5’ '3” H7 “*9”, a, O 03 "7 gun) w» 2'“ mm pm I Pix) lm —-—~ . m --.———- got) at») l 4x) ( INCLUDIN6 THE C955 IN wt)ch lm 57;) ’- i’ °° ) NOTE : THE 03:61:03). 1.1an 11051 SE 0 an INDETERDINHTE or was 3 OR “35‘ , 56-, w“ I”? m = 3 HNO 1m: 15 NOT THE X40 same as lm W90 ‘30,“), x-Qo EXBﬂPLES .' SIM-Ix --> O Jags-2): ,1. L I'" .stx —-» o = "n 5 5x :- x-vo x—vo ’05 3x a a w 363:: .2. [In T a [m --—-- : °° xgw .a, an x4” I x X I e -I -—~ 0 1m .1 "” ' BM? 3. In ‘ = 3):” x40 a O X40 '6 0 z I 4mm -——» a I sec x ~9 I ‘I. m_ x2. 7‘ m. .Zx x90 —9 0 Y‘90 DIVE —-90 .2x —9 0 77113006” NFGﬁTIUE vmuES 50 {max Im_ ,_ = " °° x-w x .1... 5 [m g-” = {m -"""""‘x f '- xé 0+ -—-—» oo x401} -cscx:o X t I 5:» X --)o I .ststx m ' """‘ = m " M“ \$901,, Xeosx _:;0 ya“ -XSWX 4-605): . 4(0)“) 0 a +1 ' 07’)?” TYPES OF INDE TERﬂINﬁTE F0305 .‘ 0.00 [M chJgtx) J l O 100 oo-°° lm chm-gun) i i, LX)"‘70 0° 1m Puma 30¢) —90 00° Inn Fix) 1“ 0° gnu—9‘9 l 'm For) THE FIRST Two TYPES ME HﬂNDLED BY ﬁLGEBIMICBLLY Tomowc THE PkooucT / DIFFERENL‘E new .9 000mm“ MD usma L'H5PITBL'S RULE. EXBDPLES .' 6. [m x INX “0*: l O am (:7)! --5~°° ~1- = lm _,_ : (m ..._‘.‘._:],p ~X:0 \$90" x “'4’ °° x-ao’ -;“;, x-w" '7 [In (l-lmvx)\$Cc.2x x-a-E' " l J a co 7- 7. " Im l-kmx ‘50 I “sax - secavr_ .2 - ‘ = m - ' ' "7" x95 Coslx a; o XA’I. 231191,: .15.”? at I I 8. [In L ‘ swx) 7 x—w" J, J, m GO _g_ smx I 1,) l 5””x ’7‘ *9 0 1 h” ( X swat smx X = m, szX —a; o x—w+ x—w I Cos x -I —9 a l - 3:» x : m —-—--——- : m ""——' xqo‘f x(osx 4, strox __9 0 x_>o+ -X\$‘NX 4- COSX +(OSX _ 0 0 : '— -' = 0 a H H 1 NOTE : THERE'S room/me INDETERnINﬁTE 68007 I Im_ (751-575;) = °° X90 1 1 oo .00 ms " ExPomENTI/BL TYPE " onrE/inwam Farms ﬁRE mamas» 8y TBKING Les/93mins, EVﬁLUﬁTING 771E LIﬂ/T OF 7715 Lose/317w), mun THEN EXPDNENTIBTIN6 To SET 7715 0316/1019). Lin/7’. EXIMPLES’ : x->°° 9. (In (""'3:L) x—)°° J l x LET y: (H é) cwswnmrropwo Im y ) x+°° E THAI J- x lny = ML”, Iny= X/NLHRL) I ML” 3%) n = _L y x (nu-lg") -)o [m lny= ['0 __,_ x—)°° X4” 2: a0 -—’r(-"i : Ian H" x x-vw vi; I l 7' x20” H§ = (+0 “I THUS, ["1 (n7 : I x9” so In)! 1 [In 7 : Iln 9- : C : e IO. N ...
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Indeterminate Forms - H L’Hémrm's RULE nEanL...

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