{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Ch4derivativesA06.mws\nThu Oct 6 08:01:01 MDT 2005\n" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "H ousekeeping Commands" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "resta rt;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "with(plots, display, implicitplot):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "with(plo ttools, disk):" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 39 "Section 4.1 - Maple and limit and Limit" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 65 "Here are some limits which don't present \+ as difference quotients:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "CompInt := n -> (1+1/n)^n;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "FarOut := Limit( CompInt(k), k=infinity); " }{TEXT -1 12 "\"Inert form\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "value(FarOut); " }{TEXT -1 38 "\"value\" helps evaluate \"algebraically\"" }{MPLTEXT 1 0 3 " " }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 13 "evalf(%, 14);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "######################################################### #######" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "divot := x -> (x ^3-125)/(x-5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "divot(5); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "limit( divot(x), x=5); \+ " }{TEXT -1 21 "Flying a bit blinded." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "######################################################### #######" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "InDet := n -> (1 -3/n)^n;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Limit( InDet(i) , i = infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%) ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "############################ #####################################" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 65 "Here's a difference-quotient limit su ch as appears on page 55-56:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "NQ := (f,t,k) -> ( f(t+k) - f(t) )/k;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "NQ(sin,Pi/2, Pi); NQ(exp,-1/100,2/100); evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "gg := x -> (x+3)/(x-5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Limit( NQ(gg,x,h), h=0);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 22 "DerivExpr := value(%);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 33 "ggPRIME := unapply(DerivExpr, x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "POTx := 2:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "POT := [POTx, gg (POTx)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "M_tan := ggPRIM E( POT[1] );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "TanLinEqn : = y = POT[2] + M_tan*( x - POT[1] );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "############################################################### ##" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 59 "Now build the sequence of plot structures to show tangency:" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "P := disk( POT, 1/25, colour=BLACK):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "delta := 3/2; epsilon := 1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "XRG := POT[1]-delta..POT[1]+delta;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "YRG := POT[2]-epsilon..POT[2]+epsil on;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "P := P, plot(gg, XRG , YRG):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "P := P, implicit plot(TanLinEqn, x=XRG, y=YRG, colour=black):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "display([P], scaling=CONSTRAINED);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 45 "Section 4.2 on Derivatives of Maple Funct ions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "gg(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "ggp := D(gg); ggpp := D(ggp);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "simplify( ggp(t) );" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "TangentLineSlope := ggp(POTx );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "########################### #######################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "D(p*q);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 " D(p/q); simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "D(p ^2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "D(p@q);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "(D@@2)(p*g); (D@@3)(p*g);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "################################## ###################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "LISTfun := [ln,sin,cos,x -> gg(2*x),exp, t -> exp(2*t )*cos(3*t)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "LISTders := map(D, LISTfun);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "LISTde rs[nops(LISTders)](0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 39 "4.3 on derivatives of Maple e xpressions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "fexpr := x*sin ( exp(3*x) );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "diff(fexpr ,x);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 59 "4.4 - Maple Implicit Di fferentiation is Different Nowadays " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 175 "As with LeastSquares, Maple ha s done some work to ease implicit differentiation, so section 4.4 of o ur text is a bit out of date. Here we demo the new \"implicitdiff\" c ommand:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "CUBIC := x^3 + y^3 = 6*x*y - 3; " }{TEXT -1 32 "Slig htly different from page 61." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "yPRIME := implicitdiff(CUBIC,y,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "yp := unapply(yPRIME,x,y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "TanSlope := yp(1,2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "TanLineEqn := y-2 = TanSlope*(x-1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "implicitplot([CUBIC,TanLineEqn],x=-3..3,y =-3..3,colour=[BLACK,RED]);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 13 " Assignment #6" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 64 "Here are the problems for Assignment #6, due Thursday, \+ 10/13/05." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 9 "Page 66: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "1(c) -- Be sure to use " }{XPPEDIT 18 0 "theta;" "6#%&thetaG" }{TEXT -1 13 " as they say." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 52 "3 -- make a blob for the point of tangency as \+ well." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 "5 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 "6" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 "12" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "16 -- use \"implicitdiff\" rather than the text's methods" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "## ############################################################" }}} {EXCHG }}}{MARK "6" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }