LogExp&InvTrig - 1H 13’ REanL THE" CORRECT...

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Unformatted text preview: 1H, 13’ REanL THE " CORRECT .. DEmeou oF In x (X > 0) : New 405 WENT TD FIND THE DEWWNWE OF THE “1910301.. 1.0633173” Powwow. In ¢x+b)- In 2: (my ... lm -——-—-,;———-— b-90 H5175 ‘s a mamas 0F In cx+b)- lax : /y=’£ Y runs, ounce evanyrmma 3y I; 79 car I ‘ Incx+b)-lnx o I am, " h x I I SINCE [m 3777, = x mm Ian 3%" = 5’? ’ THE SQUEEZE 01-” that THEMED IDPLIES mar In (ac-H; ) - In x __L IN? N: X '1 12-30 as wELL. was, Fox at > a, (lax), = 32" CoanED wmi THE CH8!» RULE THIS ewes THE 0500:. Tums : I I ( lnucu) = a?) 4'0!) Fa: i-my PosmvE FUNCTION ucx ). ac.’ (luff)’ .-. 7;“!— (6/ :w 3! “I an, EVEN BETTER’ (barf: (Inx‘i'J’: (flax) =;{-;:-= 5;; (’0Y)’= 32" FORX>0 I (In uno)’ = 1-5;, 4'00 PM #00 >0 Fol? x<o, -x>o so In(-x) I5 DEFINED/9ND C In c-:::)’: :35; c-x)’ = j— c-n = 3“- wins, (Inx)’= 3‘; Fat? x>o J. unz-m’= x Fm “0 $0 / (In Iii): 31g Fol? X#0 WITH THE cunw RULE, ’ _.!_.. ’ (In 1140‘”) ‘ am A“) I l _ E.G. , (In lszl) - smy COSX — €071)! Inx Locmnmns wmi arm-7e Bases : Iagbx : Tn—T $0 ’- .._LJ. (long) ' ["5 x 5.6. ([03,80]: 7—31; 2 (mm THE Cflmm RULE , mm 1115 198.901.4111: anUES‘, (logblunn) )’ = 75L; 4—"; A’tx) 5.6., (log3l-I'nnxl)’ = #3 5-3;; (seczx) EXPONENTIBL FUNC TIONS’ 1 In)! : X DIFFERENTIHTE IDPLICITL)’ vwm nssnscr To 1 : (/ny) ’ = nu’ —>1;-y’: I I 3 y Y' = 8" (8’0’: 6:" WITH THE CHINA) RULE \ CSCX I C56 8 ) 13.8. = e. x c—cscxcofx) I EXPDNENTIHL FUNCTIONS WITH OTIIER 30555 5 bx_ elwtlnlz. SO CbY)’: ex’nb (X’Db)’ : bxlnb ’ x ( 5“ )' : b In 5 «my ms 01mm nuns, ( hunt) I b«.m) ) : lab u'cx) Etc. z I z (5* ) = 5" [n5 tax) EXflnPLES 3 I. CDDPUTE y’ IF y: 31m (ex) ‘/’: cos (3") (e’O’: “gage” c. (3x005 (ex ) .2. ConPurt‘ y’ IF )I: Exp W+5x3 m 1 VHS»? y’= (e ) = e Mrs—pf [MSW -.L -.- e (it/*5”) z(l}5x3)’) = e ylffx3( ’5XL a. I+5x3 15xz ex_p_ Jun? .2 {usx’ x" ngx—w c H x‘)” 3. @0ow y’IF )l: l"( smpury FIRST .’ 3 Y = In (xz {ax-m)- In (”XI-)7 J- : Inax‘) 4 In arm)? —- Vlncux‘) = .2 In x + g- In l‘7x-I‘U - ‘l ’0 (""27 I ' I J- } (7x—M)’— 4 -—’ “”9 y’: 2(3'2')* 3 vx-u/ ”X‘ 7‘ 3nx-m) HX‘ x‘3'7x M q. conPwE y’ IF 7 = ——-;'—.," (Hx J LDGHIPITHI‘IIC DIFFEREMMWM: mm; In or 1307'» $1055, DIFFERENTIBTE IflPLICITL)’ mun SOLVE FoR y ’ . 5. 3 7‘1 1/ 7x-Iq km) 7‘ “any: =5 lny = ln( un‘v" Iny = Jinx + g-Inwx-M) - Vlnum‘) DIFFERENTIBTE : '7 9x I / _. .2 __ _ 7y ' 3? *3z'7wi) ”xi- 9): q I .1 __ Y = ( 3': 4’ sou—nu HI“ )7 I . .2 ‘7 __flr_ ) *2 V’Ox-n/ y ' ( 3? * 319x40 Hat “”1” swx y = x smut My : In (X ) 'ny = csw nun x) >’ ‘LY’ = tswa'é' ) 4 Un)‘)(Cosx) y’ = (a?! 4- Unx)(msx) )y 3‘ VI. (SINK 4' ‘Inx)(£O$X))X S’ln X RECBLL 2 arcmu x a ANGLE») (-35 E ) «moss mmzm 15x y: nrcsee x = may; no [0. {no (3”,?!) wmxe‘ 56mm IS x DERWHTIVES : y : nrcsw x smy=x omensmmns mmcmy mm: nesrec‘r w x : I sty)’ = (X) (casny' = I smnmmy, consuoED wm: THE Ch‘mm RULE we GET THE mum. THING : ' l I w a M LXI chrc’fimutm) ' + “u: I l I - M l!) (Arcsec aunt!) ' Mug” («unfit EXHDPLES 1 3 ’ I tX’)’ " 3x1 I, {arcsm (x )) = J‘: cx’)‘ ‘f; .. x; x I e I I X)’ - z: nrc sue“ ) = ‘8 " X 7- J "‘ - .z_ t S ) WWW e ex... e I 3. Fax) : In (nrcIm-fi) => I P1X): ’ (”(313%)”) 9mm» 4x I l I I ,— ’ _..__.' ' WNW luff)” 6“:th H x 4“” I QR ( liX)fiPCIflIU\/? I! 4. pm») fiLL wawe‘s 0F x m‘ wmcy 7/ : graham u") M; A Homeoumz. TfiNGENT LINE. I . I ”‘1’! :- 4X 7 ' 1+ “‘2‘ Hx" y’:o =1; 4" =0 =>4x=o => x=o Hx" IO. L. 5. FIND y’ 3y InPucn' amrsksmmmm 1F fircsw my) = firccas Lx-y ) (Arcsw cxy))’ = cameos cx «yn’ I I -——-—~ cxy)’ , I r—-—-—- = ~ -—-—---" ax - "IXV’L "3,, (x.y)'- y l "-1—— ny’+y) = o """""'—""' Ll'yl) inc-3")" \Ilwtx'yfl' ' I X I Y + 7*” I W IJ-x‘y‘ - ' VNWJ‘ Wax->0" y DULTIPLY 7713006” 8V dlvx‘y" Vl-m-y)" : / ah/h zx-y)‘ y’ +y/J-Lx-y)‘ = - JI-x‘y‘ + (I—x‘y‘ y U‘W'm-y)‘ ~W~x‘y“)y’ = ’W'xty' ‘yVl-nc-y)‘ yW-w—y)“ + l-x‘y‘ , - .. W - 7 xJa-cx‘y)‘ - hex‘y‘ dz FWD 3% u: )1 : nrccoscsx) ‘ 3 d I (“3’ --—--—-~ ally 3 ' .J I '3}? (' m) = fiat-ext”) in; ’ = - (-éu-q ‘) ‘u-qx‘) ) r'lw X -3]; Lh‘lx") (-1830 = ~4'7x (I-ex”) H. ...
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