with(plots) : Příklad 6 multiple(plot,[{seq{[n,n/{n + 1)], n = 1 ..30)},jc = 0..20, style =point, symbol = cross, symbolsize = 20], [ 1, x = 0 ..30, color = blue, thickness = 3 ]); i,u- ++ + ++++++ 0,9- + 0,8- + - + 0,7- - + 0,0- 0,5- + i i i i i 10 20 30 Příklad 7 multiple{plot, [{seq{[n,root[n]{2)],n = 1 ..30)},a: = 0..20,style =point, symbol = cross, symbolsize = 20], [ 1, jc = 0 ..30, co/or = W«e, thickness = 3 ]); 2,0- + 1,3- 1,6- 1,4- + - + 1,2-1,0- + ■ i ' +++++++++++4 i ' i 10 20 30 Příklad 8 multiple(plot, [2Ax,x = 0 ..5, color = red, thickness =3], [xA2, x = O ..5, color = blue, thickness — 3]); F~ = { ln(2-x3 + 4- x2 - x) ' (jc + 1) Fl ■■= diff(F,x); Příklad 11 6x + 8jc- 1 F2 := diff(F,x$2); {2x3 +4x2-x) {x+ 1) 12* + 8 ln(2jc3 + 4x2 -x) (x+í)2 (6x2 + sx- l)' {2x3 + 4x2- x) (x + 1) (2*3 + 4x2 - xf {x + 1) _ 2(6x2 + 8jc- l) 21n(2x3 + 4x2-jc) (2x3 + 4jc2-x) (*+ l)2 (x+í)" plot(F,x = O ..5, thickness = 3); with{Student[Calculus 1 ]) : DerivativePlot (F, x = 0.9 ..5, thickness = 3); The Derivative of , lnÍ2í3+4í2-í-) rl = —!----------------------- x + \ on the Interval [0.9, 5] f(x) ^-^ 1 st derivative plot([F, Fl, F2],x = 0.9. .5, thickness = 3, color = [red, blue, green], legend = ["Původní funkce""!, derivace", "2. derivace']); ■ Původní funkce ^^— 1. derivace ■ ■ 2. derivace F[l] •= eval{F,x = -i); \ ¥5) Fl[\] ■■= eval{Fl,. t = l); 10 4 K ' F2[\] ■■= eval(F2,< í = 1); 67 l 1 řO evalf(F[l]); 0.8047189561 evalf(Fl[l]); 0.8976405221 evalf(F2[l]); -2.27764052: with(student) : showtangent (F,x=l,x = 0.5 ..5, thickness = 3, co/or = [cyan, red]); showtangent {Fl,x = 1,x = 0.5 ..5, thickness = 3, color = [cyan, blue ]); showtangent (F2, x = 1, x = 0.5 ..5, thickness = 3, color = [cyan, green]);