GSPkl FE1capm#dtz:?  AV1_hldCondensedI PPcnion CondensedMinion CondensedItDpB %tv{A`FľQ&u#. FeݾGHsFtľQ&t&CC totH9X~1CC tW\F'F   IN /CC t@Ea~jDh!u5$W)vuWjh(h u_^[]U1CC tEgH9X~CA t:?alps H9X~CpB tf 7 mR_N LMM_@ 0 = 0 = tlq  AQ V{`Vw Vw Vw HoBoDp CB dtP+e  %GIhVV0%FIhJ@J-IV04Can you adjust delta so that when x is within delta of c, f(x) will always be within epsilon of L? Try with different values of c and epsilon, to make sure it's always possible. Tabulate your results for c, L, epsilon and delta.t){? %Ihڪ W9W9W=J`u*Adjust the sliders to change the function.t AW.ph Ҁ Ұf(x) = ax{u:2} + bx + cC t9?oB t AE Expert DisplayMinion Ext Display ItalicMinion Expert ItCpBDpB? $t\B6B. ݾIJw&م&ص^F&؍&ح^FCC t'o,tB H'9X~CC t%W*\B F'   IN CC t'@,EB D'!u5$W)vuWjh(h u_^[]UCC tB H'9X~DA t:?B H'9X~DpB #t N N. 2CoordSys܎uݞ}݆}f^݆}f^ŐF՛Nnݛ^CCK@t!ntn1CCCC? t!V\lXBC.CC6KKKBx>C/CCCC? t!?E~hjS &a~jW&a~PVW&a~jj}P1CCCC? t!nCADA? t!9?nCpBDpB? tD_kooBmPCourierCourier New PS MTFranklin GothicGenevaGeorAB = Distance(A to B) = t? H'9X~CA tx}@ H'9X~DA t> H'9X~CA tx:}?@ H'9X~DpB tW\@ F'   IN CC tsoxt H'9X~BC "tC~ N 5?yI^ 5O5T'=oCCChBף? "t N 4?x%o=o=ե'?%o= =t o= =%o=ꦠ5o=0CCDC`? tsoxt IBC tW\@ G? BCuK  1FzPCC t@E? Et$Pt$ J/D a~t$Pt$X<@L$_^ VJmCC tx}@ IDA tx:}?@ IDpB t@  BARKX@LIK CC t?D  BASW${IhW WCC t6;`@  BAT0?0JJOJ|Jl;JhiJy@  DC tch BAU* XPX*Ih QXX*Ih BC tK1DAnimate delta Bi8+))Bh\^Bh' QQ' t,1ff  x(min)mJP 8+*,x{l:min}o}]NJ9oUo8BC"t?  x(max)mJP 8+*,x{l:max}i}]NJ9i4i0DC"tvc   = c = # trntoBC1CC? #t\rb  ? FV`  = b = $ tV\m BCXBCuK6uK6KZ}>CCC/CC? $tF\Nu֡aha~%a~F^VWha~d%a=a~tLa~0~,3a~Ha~49  = a = % t?Ea~kWt$|$W.VW%ps,%a~_^[ t$t$T$pr,JmCC1CC? %t c   = c = & t}oDACA? &ta0c   = c = ' t9}? oDpBCpB? ' t+ff?m8BC0DC? .-t24' mW)@IhLRmPRm) {D:c}{10} = e =  5tE\4' mW)@IhLRmPRm) {D:c}{10} = d =  7t?  cmJP 8+*,*,m}]NJ9m mCC9tf=*4mSI{| } Text Format  delta{!:*}AB = delta*Distance(A to B) = ;tf&TA4mTI{| } Text Format  epsilon{!:*}AB = epsilon*Distance(A to B) = :t*m3x: Coordinate(Point x): <t +x..:O^LCsx CC <=tI@ +x..:O^LCsx CC <=t  Case 1mJP 8+*,*,E}]NJ9EpE '&(<t  Case 2mJP 8+*,*,U}]NJ9UvU ')<&t  Case 3mJP 8+*,*,g}]NJ9gqg  Not'&*<t  Case 4mJP 8+*,*,O}]NJ9OO '&+<tW' gAx ppppppppppppp x{l:x} = x ->  ?tf=XmUJ`JFw Jalues x: Coordinate(Point x): AtfmXJJŠ0JPCCx: Coordinate(Point x): @tgA mAHI{| } Text Format  x{l:c} = c = ?tZ gAmQf0N LMM e a{!:*}x{u:2} + b{!:*}x + c = lim f(x) =  ? 3F1/tfTr gAmV JPJ J@HJPJ  = x1 = Gtf gAmYJPJ NonexistingJ0JJҴ JJ0  = x2 = Htsuah ;AK BTBookmanChicagoCourierCourier New PS MTFraCxC JFtv{suah ;LJ~oJJ}Jz`J9JsJ~vJCxCJtfkgAmWJJ0JJ a{!:*}x{u:2} + b{!:*}x + c = f(x1) =  3K1/tfgAmZJJ0J ? a{!:*}x{u:2} + b{!:*}x + c = f(x2) =  3L1/t0 gA mAIH@L H (lim f(x)) = L = J't'(?AK BTBookmanChicagoCourierCourier New PS MTFraM(9<?FJMtJ ;AMJpJ0XCC%L<C>C OKt}J  ;ANCJJCuCCCKDJ@PJJ<JCB PLtv{suah ;AO BTBookmanChicagoCourierCourier New PS MTFraC>C Otv}{suah ;AP BTBookmanChicagoCourierCourier New PS MTFraCB Ptv{? +ALBTBookmanChicagoCourierCourier New PS MTFraCxC N>tv{ɿ +ALBTBookmanChicagoCourierCourier New PS MTFraCx*C N>t hgAmABI{| } Text Format  (1 + sgn{(:epsilon {@:f(x1) f(x)}} = '1 + sgn[epsilon abs[f(x1) f(x)]] =  ,6:OJtb3D gAmACM  M`MR0 (1 + sgn{(:epsilon {@:f(x2) f(x)}} = '1 + sgn[epsilon abs[f(x2) f(x)]] =  ,6:PJ tse pB`KEK%K&0KE Condensed?gniDCCCBC>CCC@TSA tx pC Find FileGlobal Vage Fax CenterGraphing Calcula?giJCBCBC>CC>CTVUS tu{  AD& Ih UkUl&IhmmmmUkmmmmmCxCCx*C? XWQtpLkggAmAEKN LM M`K d{(:1 + sgn{(:epsilon {@:f(x1) f(x)}}}{!:*}{(:1 + sgn{(:epsilon {@:f(x2) f(x)}}}{!:*}0.06" = V(1 + sgn[epsilon abs[f(x1) f(x)]])*(1 + sgn[epsilon abs[f(x2) f(x)]])*0.06" = @p=YZtlq +AQ V{`Vw Vw Vw HoBoDp CB  ^atTgAmAFff33̙KT p0.24" {(:{(:1 + sgn{(:epsilon {@:f(x1) f(x)}}}{!:*}{(:1 + sgn{(:epsilon {@:f(x2) f(x)}}}{!:*}0.06"} = `0.24" ((1 + sgn[epsilon abs[f(x1) f(x)]])*(1 + sgn[epsilon abs[f(x2) f(x)]])*0.06") = Aq=^t] cB BTBookmanChicagoCourierCourier New PS MTFraCBp=AF%5?F%5? _tlq +AQ V{`Vw Vw Vw HoBoDp ףCB  ` t]PV within epsilon 8+*,*,}]NJ9n?CBףCBat] cC%Ih V V@%IhV CBp=AF%5?F%5? bt]pHideymbol Tekton MM Tek MM OblTimesTimes New Roman UnivectF YShowTBookmanBrush Scri DChicago Comic Sans MS   MTc t]PV not within epsilonJ~oJJ}Jz`J9JsJ~vJى?CBףCBdt2EHideymbol Tekton MM Tek MM OblTimesTimes New Roman Univegt2ShowTBookmanBrush Scri DChicago Comic Sans MS   MTgt.}Hide indicator Bi8+))Bh\^Bh  eht.j}Show indicator Bi8+))Bh\^Bh  fit.WjAnimate delta Bi8+))BhA\^BhAhA  ,kD'Symbol9X~Arial( 7