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" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 14 "f:= x^2-3*x-4;" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 10 "f actor(f);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 10 "plot(f,x); " }}}{EXCHG {PARA 200 "" 0 "" }{PARA 200 "" 0 "" {TEXT 204 89 " W hen we wish to evaluate an expression for a specific numerical value o f x, we must" }}{PARA 200 "" 0 "" {TEXT 204 23 "use the \"subs\" comma nd." }}{PARA 200 "" 0 "" }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 12 "subs(x=2,f);" }}}{EXCHG {PARA 200 "" 0 "" }{PARA 200 "" 0 "" {TEXT 204 90 " The standard mathematical notation would be f(2) . \+ We can use this notation in Maple" }}{PARA 200 "" 0 "" {TEXT 204 47 " if the expression is set up in a different way:" }}{PARA 200 "" 0 "" } }{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 17 "f:= x->x^2-3*x-4;" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 5 "f(2);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 19 "f(.5); f(0); f(-3);" }}}{EXCHG {PARA 200 "" 0 "" }{PARA 200 "" 0 "" {TEXT 204 61 " When defined in this way , f is called a function in Maple." }}{PARA 200 "" 0 "" {TEXT 204 75 "Functions must be entered differently in certain commands, such as plot and" }}{PARA 200 "" 0 "" {TEXT 204 7 "factor." }}{PARA 200 "" 0 "" {TEXT 204 1 " " }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 13 "pl ot(f(x),x);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 13 "factor(f (x));" }}}{EXCHG {PARA 200 "" 0 "" }{PARA 200 "" 0 "" {TEXT 204 80 " \+ The function notation is handy if , for example, we are investigating limits:" }}{PARA 200 "" 0 "" }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 26 "f:=x->(sqrt(x^2+9)-3)/x^2;" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 19 "f(1.);f(.1);f(.01);" }}}{EXCHG {PARA 200 "" 0 "" } {PARA 200 "" 0 "" {TEXT 204 62 " The \"for\" command is useful for g enerating multiple values." }}{PARA 200 "" 0 "" }}{EXCHG {PARA 200 "> \+ " 0 "" {MPLTEXT 1 205 43 "for n from 0 to 2 do f(10.^(-n)) end do;" }}}{EXCHG {PARA 200 "" 0 "" {TEXT 204 1 " " }}{PARA 200 "" 0 "" {TEXT 204 35 "The \"limit\" command is interesting." }}{PARA 200 "" 0 "" }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 19 "L:=limit(f(x),x=0); " }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 26 "f:=x->(sqrt(x^2+3*x +1)-x);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 19 "plot(f(x),x= 0..20);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 40 "for n from 1 to 4 do f(10.^n) end do;" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 23 "limit(f(x),x=infinity);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 22 "limit(1/(x^2-1), x=1);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 22 "limit(tan(x), x=Pi/2);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 13 "f:=x->sin(x);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 19 "m:=(f(x+h)-f(x))/h;" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 13 "limit(m,h=0);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 8 "abs(-3);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 21 "f:=x->abs(x-3)/(x-3);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 13 "plot(f(x),x);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 16 "limit(f(x),x=3);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 21 "limit(f(x),x=3,left);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 22 "limit(f(x),x=3,right);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 20 "limit(sin(x)/x,x=0);" }}}{EXCHG {PARA 200 "" 0 "" }{PARA 200 " " 0 "" {TEXT 204 79 " The \"piecewise\" command permits you to cre ate piecewise defined functions." }}{PARA 200 "" 0 "" }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 38 "piecewise(x<1, x, x=1, 4, x>1, x^2-1) ;" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 44 "f:=x->piecewise(x< 1, x, x=1, 4, x>1, x^2-1);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 17 "f(1); f(0); f(5);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 19 "plot(f(x),x=-1..3);" }}}{EXCHG {PARA 200 "" 0 "" }{PARA 200 "" 0 "" {TEXT 204 40 " More practice with \"limit\" and \"plot\"" }} {PARA 200 "" 0 "" }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 26 "f:= \+ sqrt(2*x^2+1)/(3*x-5);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 23 "plot(f,x=0..6,y=-2..2);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 21 "limit(f,x=-infinity);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 20 "limit(f,x=infinity);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 15 "limit(f,x=5/3);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 19 "f:=(x^3-1)/(x^2-1);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 12 "simplify(f);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 2 "f;" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 13 "limit(f,x=1);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 12 "f:=fl oor(x);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 16 "plot(f,x=-4. .4);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 13 "limit(f,x=2);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 18 "limit(f,x=2,left);" } }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 19 "limit(f,x=2,right);" } }}{PARA 201 "" 0 "" {HYPERLNK 206 "Lab 2 Homework" 4 "math.asu.edu/~od ish/Lab 2HW.htm" "" }}{PARA 201 "" 0 "" }}{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }