{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Techniques for Computing Limits

# Techniques for Computing Limits - TECHNIQUES 5:313 ConPurmc...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: TECHNIQUES 5:313 ConPurmc EXﬂnPLES : I, [m X1: 3"“3 X—‘r3 Lmn‘s a. lm (xhax) = {-1)1+Ql-I)=-l 'X-ﬁl-l Pouwomms : lm X—Ma. Pix) = anxn+ ---+a.x 440 Pm = Pm.) n = “If!“ +~“+Q‘a-+qa xz-ax —-+ 32— .us) = 3 3. Im an : .3. 15—93 ' “’1 3+I -'- H a z z , X-HJH3 --+ :-%J+3.=o a ‘L 'I” 7““ 1 = —— = a 1—H x--.?x~3 ...., i-au)-3 s-..) .q x1— .17: ~3 -—-» #1 5. Im ._.._.....—--— a so THE leT 0055' Mar EXIST 3197:0an FUNCTIONS : Fax) nun 0w) PaLynomeLs_ Pu) P I!” ) '.-. 4‘21!- UNLESS aid) :0 2-54. an: 6? 4) IF QM) = 0,1301 Pm.) #0, THE anr 0055 N07 EXIST. IF GM.) =0 am; PM.) = 0 THE L101?” 15 53:0 To BE woarerenwmf 9f TVPE O .— 0 ant) 7108!? we“ IS REQUIRED To DE JEWINE TmE umr 5.8., an 0F THE Fouowwc ﬁes :moETERmnMJE ,m X’ , .36.. , .53 I 5X’ _:k—- . In 3 H1 3 "1 3 I “‘3' 4“) H = (m M4? 1 3 so me Lmn ONE. 39.4,, Xvi —--Ip 1—! = 0 l 42): H n .-. )c-l-u" x1—: I,” 43:?! = ’69 - x14 7.‘ 1m THIS was 7717? “EUR/9 may " REQUIRED To DErErinwE THE erT '5 PRETTy oBVmUS : I FACTOR awn CHNCEL [m xz—ax-z I n = I X-‘93 Xqu *3 3:493 = 1m 1-33 . 3+ - “—3-; £3+9 I —9 O 8' £31,”; £+1 do I {ﬁnal—MM) = In M H”; but :2 III? (tl'u*q) .t-w- —_ c—n'zu—uw = u. cx-3)cx H J Lx-szcx-U NOTE : camcELst ms x—3 nEAms owwwc munERBTOR 3ND DENanmgmg 3y X-3. THIS IS kEcmnm'E 3565055) no rm x¢3' x-pa BECBLL : 19533 33-83 = (HENRI-331F313 .-. {19-5) m‘HJB +32 )- (Jung-9 ‘ —-> o 9 'm -"'_——“"' ham h a a T815 "runs :1 15 Woman 5851557“ 7'0 EXPrmD ' 3 mung-9 (8+l-117461114L’7J-8 hn “37—" = 3m W5 have 5‘99 . 1314053“? “’4405451) : hr: ““7"” = 1'" I, h—ao ' (“'30 .-. lm unwind") =. 1146-040?" :12 h-ﬂo I'X " "‘5’ O 10. [In x a 0 1+0 THE STﬁWDﬂ/c’D THING TE? DO WITH [9 SQUHEE ROOT IN I? SUI“) OR DIFFERENCE I; WE ' 1 2. - -l l 1—): -J ' Iii-x -I JI-x H In (F?) n = m ---—'—"'" = a thr H) 3:190 1‘ Xe» 3‘ W“! H x-aa x l-x -I " l " _ [m ‘— [In M ‘= m .__.....—— " Tum—H) x—yo XUVV H). x-ao “-3! 4" X-‘JO - l .__—--'——' = .- _L {3-0 H ’~ ‘I H. Ll. [In \$.30 1" --*.~ 0_ w E ConPLEx FRHCTIOAJ ' -—-'- .. J. I -..L 1. _lm ‘1“ " 9- : [m am”; i um) I?” *‘w 1: aczm‘) . (m J-cau‘) I ~46?“ .. ' m 16—90 Mani?) PM .21; an?) ' 1m 6.2.5..— ‘9' 0 6 AH, aunt) ._.,,, - ”J = 0 ,3... x“; F at”, , (. : X) “1'5 , n1 2- x s: 3 ”“3 x > 3 I hn_ch)= Im_:;;3:_oo ’9’“?- x—‘a-z 7. lm PLX) =~ lm (X135) '-'- (-1) -5 = -’ “*‘f 1-3-2 1. ' _ 7- , 7’ _5. lm Pm) - Im (at —5') _ o as x40 xaa z 1 __ lm pa) = Inn- (x ~5)=.3-5,q THUS) X-‘IS' ”1-93 pt [In X)="I '10 Put) .- lm *1/1413 = u/3-ug .6 1+3 x-os _ ...
View Full Document

{[ snackBarMessage ]}