00020001010008main.ACT00030200072^x.EAC010000003fe8"^\:IR[Introducing a special[number.[[ Example One:[Compare some values of[2xand 2xxfor[corresponding values of[x.[\tangent at a point``vrALCuxyH# `G6!`shB`BRc `G6 `6!0`!&0`1WG@`G6 YcxpYcxp G6 1WG@!&06!0G6 BRc shBG6!`P 2P I11 GWP 2Hp 4#1P 2 xDP 8P wW0 1Pp v3rU%1HQWtEpP7d BE%%fTvq ! 5H  H  A@6%`%VYS6   2^x%``&1WG7 1@  9[-50.03125 0.02166084935 -4.473684211 0.0450077043 0.03119696325 -3.947368421 0.06482219028 0.0449313183 -3.421052632 0.0933599351 0.06471217575 -2.894736842 0.1344613233 0.093201487 -2.368421053 0.1936574553 0.1342331185 -1.842105263 0.2789144794 0.193328785 -1.315789474 0.4017056133 0.2784411125 -0.7894736842 0.5785551186 0.40102385 -0.2631578947 0.8332620064 0.5775782123 0.2631578947 1.20010272 0.8318550167 0.7894736842 1.728443787 1.198076338 1.315789474 2.489385179 1.72552531 1.842105263 3.585328385 2.48518183 2.368421053 5.163756792 3.579274457 2.894736842 7.43708284 5.155037642 3.421052632 10.71123281 7.42452525 3.947368421 15.42681597 10.6931466 4.473684211 22.21841828 15.40076712532 22.180902\ List EditorGraph2D@ Graph3DT LISTCAL`, LISTSYS4NModify $ STATCALC NSTATSYS \NSequenceH, Sheett| Sheet3D| SolveEqlSolveLwrp SolveUpr| StupFLG1(StupListD StupPict$ ViewWind 4 @ L X d p |            ! " # $$ %0 &< 'H (T )` *l +x , - . 0 1 2 3 4 5 E F H I J K, L8 MD NP O\ Ph Qt R S T ]D ^D _,D `pD a b       list3/list2system]listsystem^]=system_^system`_systema`systemb~ aseq_histbNewFolde system]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=systemsystem]listsystem^]=system  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i "^\:I $ `P`P`p`p `(10qy`#YuY  $0<HT`lx G6!`shB`BRc `G6 `6!0`!&0`1WG@`G6 YcxpYcxp G6 1WG@!&06!0G6 BRc shBG6!  $0<HT`lxP PpC H" 3YQ 4F#0 etU0 xDy@ pV0 xUQ` 3& @  rrCxpHXS(8P7Vy Cp#(T&Yp"A   $0<HT`lx`P 2P I11 GWP 2Hp 4#1P 2 xDP 8P wW0 1Pp v3rU%1HQWtEpP7d BE%%fTvq !  $0<HT`lxqy qxX  qxT q  qyR qw'x qQ qxc2 qW 14 1E 1ix 2 14$ 1P 1P 1P 1D3 1rUy 1P ` P[[**What is list3/list2?R2^xxR2xln2Rln2R 0.6931471806R[ Exercise One.[Insert a Graph Editor[strip and explore the[ functions axand axx[where a=2.2, 2.4,[2.6, 2.8 and 3.[For each function[compare the value of[the function and the[derivative at the same[ value of x.[What do you notice?[Now insert a List Editor[and investigate in a[similar way as shown in[ the example.[[ Exercise Two.[Insert another Graph[Editor strip or List[Editor and experiment[to find the value of a[in axand axx for[which ax=axx.[[Exercise Three.[ Now consider axx.[You should be confident[from the previous[exercise that this[function is an[exponential function.[But exactly what[ function?[Use your previous[findings to make a[conjecture about[axx.[[Once you have made a[conjecture, you can[check your result using[the computer algebra[capabilities of this unit.\Check your conj. $RaxxGraph2D, Graph3D@ LISTSYSL4NModify $ STATCALC NSTATSYS \NSequence, Sheet4| Sheet3D| SolveEq,SolveLwr0 SolveUpr< StupFLG1H(StupListpD StupPict$ ViewWind     $ 0 < H T ` l x       ! 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