{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 59 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "f:= x -> x^(a-1)*(1- x)^(b-1)/(int(u^(a-1)*(1-u)^(b-1),u=0..1));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "a:=2; b:=3; plot(f,0..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(D(f)(x)=0,x);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 277 "a := 'a': b := 'b' : solve(D(f)(x)=0,x); simplify( D(f)(x)=0);\n(1-x)^b*(-x^(a-1)*a+x^(a-2)*a+2*x^(a-1)-x^(a-2)-x^(a-1)*b )=0;\n-x^(a-1)*a+x^(a-2)*a+2*x^(a-1)-x^(a-2)-x^(a-1)*b=0;\nsimplify((- x^(a-1)*a+x^(a-2)*a+2*x^(a-1)-x^(a-2)-x^(a-1)*b)/(x^(a-1))=0);\nsolve( a*x-a-2*x+1+x*b=0,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "as sume (a>1, b>1): solve(D(f)(x)=0,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "a:=1/2; b:=1/3; plot(f,0..1);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 73 "plot(f,0..1,numpoints=2000); limit(f(x),x=0,ri ght); limit(f(x),x=1,left);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "7 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }