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" }}{PARA 203 "" 0 "" {TEXT 210 0 "" }}{PARA 203 "" 0 "" {TEXT 208 3 " " }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 212 39 "Expressions versus Functions in Maple" }{TEXT 212 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 200 57 "We have seen that expressions \+ are easy to use in Maple. " }{TEXT 200 0 "" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 14 "f:= x^2-3*x-4;" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 10 "factor(f);" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 10 "plot(f,x);" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 210 0 "" }} {PARA 203 "" 0 "" {TEXT 208 89 " When we wish to evaluate an expr ession for a specific numerical value of x, we must" }}{PARA 203 "" 0 "" {TEXT 208 23 "use the \"subs\" command." }}{PARA 203 "" 0 "" {TEXT 210 0 "" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 12 "subs(x=2,f); " }}}{EXCHG {PARA 203 "" 0 "" {TEXT 210 0 "" }}{PARA 203 "" 0 "" {TEXT 208 90 " The standard mathematical notation would be f(2) . We c an use this notation in Maple" }}{PARA 203 "" 0 "" {TEXT 208 47 "if th e expression is set up in a different way:" }}{PARA 203 "" 0 "" {TEXT 210 0 "" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 17 "f:= x->x^2-3 *x-4;" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 5 "f(2);" }}} {EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 19 "f(.5); f(0); f(-3);" }}} {EXCHG {PARA 203 "" 0 "" {TEXT 210 0 "" }}{PARA 203 "" 0 "" {TEXT 208 61 " When defined in this way, f is called a function in Maple." }} {PARA 203 "" 0 "" {TEXT 208 75 "Functions must be entered differently \+ in certain commands, such as plot and" }}{PARA 203 "" 0 "" {TEXT 208 7 "factor." }}{PARA 203 "" 0 "" {TEXT 208 1 " " }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 13 "plot(f(x),x);" }}}{EXCHG {PARA 203 "> " 0 " " {MPLTEXT 1 201 13 "factor(f(x));" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 212 6 "limits" }}{EXCHG {PARA 203 "" 0 "" {TEXT 210 0 "" }}{PARA 203 " " 0 "" {TEXT 208 80 " The function notation is handy if , for exampl e, we are investigating limits:" }}{PARA 203 "" 0 "" {TEXT 210 0 "" }} }{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 26 "f:=x->(sqrt(x^2+9)-3)/x ^2;" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 19 "f(1.);f(.1);f(.0 1);" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 210 0 "" }}{PARA 203 "" 0 "" {TEXT 208 62 " The \"for\" command is useful for generating multiple values." }}{PARA 203 "" 0 "" {TEXT 210 0 "" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 43 "for n from 0 to 2 do f(10.^(-n)) end do;" } }}{EXCHG {PARA 203 "" 0 "" {TEXT 208 1 " " }}{PARA 203 "" 0 "" {TEXT 208 35 "The \"limit\" command is interesting." }}{PARA 203 "" 0 "" {TEXT 210 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f:= x->x^2 -3*x-4;" }{TEXT 211 0 "" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 19 "L:=limit(f(x),x=0);" }{TEXT 210 0 "" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 26 "f:=x->(sqrt(x^2+3*x+1)-x);" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 19 "plot(f(x),x=0..20);" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 40 "for n from 1 to 4 do f(10.^n) end do;" } }}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 23 "limit(f(x),x=infinity) ;" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 22 "limit(1/(x^2-1), x =1);" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 22 "limit(tan(x), x =Pi/2);" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 13 "f:=x->sin(x) ;" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 19 "m:=(f(x+h)-f(x))/h ;" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 13 "limit(m,h=0);" }}} {EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 8 "abs(-3);" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 21 "f:=x->abs(x-3)/(x-3);" }}} {EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 13 "plot(f(x),x);" }}} {EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 16 "limit(f(x),x=3);" }}} {EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 21 "limit(f(x),x=3,left);" } }}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 22 "limit(f(x),x=3,right); " }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 20 "limit(sin(x)/x,x=0) ;" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 212 19 "piecewise functions" }} {EXCHG {PARA 203 "" 0 "" {TEXT 210 0 "" }}{PARA 203 "" 0 "" {TEXT 208 79 " The \"piecewise\" command permits you to create piecewise def ined functions." }}{PARA 203 "" 0 "" {TEXT 210 0 "" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 38 "piecewise(x<1, x, x=1, 4, x>1, x^2-1) ;" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 44 "f:=x->piecewise(x< 1, x, x=1, 4, x>1, x^2-1);" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 17 "f(1); f(0); f(5);" }}}{EXCHG {PARA 203 "> " 0 "" {MPLTEXT 1 201 19 "plot(f(x),x=-1..3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 211 105 " Use the command floor and examine the output. 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