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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Centroid" }}{PARA 0 "" 0 "
" {TEXT -1 84 "Exercise 1. Find the centroid of the function f and g b
elow with specified interval." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 16 "f:=x->(x-2)^2+2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "p
lot(f(x),x=-5..5,y=-10..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 17 "g:=x->-(x-2)^2+3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "
plot(\{f(x),g(x)\},x=-5..5,y=-10..10);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "fsolve(f(x)-g(x)=0,x,0..4);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 48 "My:=proc(a,x,p) int(p*t*(g(t)-f(t)),t=a..x) end;
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 48 "Mx:=proc(a,x,p) int(p*(g(t)-f(t))^2,t=a..x) end;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "M:=proc(a,x,p) int(p*(g(t)-f
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30,2.7,2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Mx(1.30,2.7,2
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f:=x->sin(exp(x));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(f(x),x=-5..5,y=-10..10)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "g:=x->cos(exp(x));" }}
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y=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "My:=proc(a,x,p
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0 "> " 0 "" {MPLTEXT 1 0 27 "fsolve(f(x)-g(x)=0,x,0..2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "My(0,1.36,2);" }}}{EXCHG {PARA 0 ">
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1 0 25 "Mx(0,1.36,2)/M(0,1.36,2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
25 "Exercise 2. [a,b]=[-4..?]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 28 "fsolve(f(x)-g(x)=0,x,-4..0);" }}}{EXCHG {PARA 0 "> " 0 "" 
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