http://yktlab.cis.k.hosei.ac.jp/wiki/ 1(Plot) f x x x 1 1 x x ( )[( 1)_, ( )_, ( 3)_,...]=( ) Plot Plot f x, x, 5, 3 15 10 5 Plot[( ), {( ), ( ), ( )}] D g x x 3 x 3 Plot f x, g x, x, 10, 8 00 100 10 5 5 100 00
GraphicsWithPlotFull.nb Plot[{( 1), ( ),...}, {( ), ( ), ( )}] Plot Plot Cos x Sin x, x, 5 Π, 5 Π, AxesLabel x, y 1 15 10 5 5 10 15 x 1 Plot AxesLabel->{x, y} AxesLabel->{(x ), (y )} Plot Sin 1 x, x, Π, Π, Axes False Axes->TrueAxes->False Plot Sin x, Sin ' x, Cos ' x, x, Π, Π, PlotStyle Green, Red, Blue 0.5 3 1 1 3 0.5 PlotStyle->{Green, Red}
GraphicsWithPlotFull.nb 3 Plot x, Log x, x, 4, 4, PlotStyle Dashed, Thick 4 4 4 6 PlotStyle {Dashed, Thick} Plot Sin x x, Sin x x, x, 4, 4, Filling 1 3 1 4 4 1 3 Filling {1 {}} Mathematica 1-1 f x Exp x Exp[x] f x Exp x x
4 GraphicsWithPlotFull.nb Plot f x, x, 10, 10, AxesLabel x, y 1500 1000 500 10 x 1- f x Sin x g x Cos x h x Tan x Sin[x], Cos[x], Tan[x] f x Sin x ; g x Cos x ; h x Tan x ; Plot f x, g x, h x, x, Π, Π, Axes False Pi Π 1-3 f x Log x g x f' x h x f'' x
GraphicsWithPlotFull.nb 5 Log[x] '[x], f''[x] 1 f x Log x ; g x f' x ; h x f'' x ; Plot f x, g x, h x, x, 10, 10, PlotStyle Red, Purple, Yellow 1 10 5 5 10 1 1-4 f x Exp x x x 1 x = 1 f'[1] y=g[x] g x f' 1x 1 f 1 1 x Plot f x, g x, x,, 4, PlotStyle Thick, Dashed 0 15 10 5 1 1 3 4 5
6 GraphicsWithPlotFull.nb 1-5 f x x x 1 g x x f x x x 1; g x x ; Filling Plot f x, g x, x, 5, 3, Filling 1 15 10 5 4 5 (ContourPlot Manipulate) ycontourplot ContourPlot x y 1, x y, x y 3, x y 4, x,.,., y,.,. 1 0 1
GraphicsWithPlotFull.nb 7 ContourPlot ContourPlot[{( 1), ( ),...}, {( 1), ( 1 ), ( 1 )}, {( ), ( ), ( )}] Plot x y ContourPlot ContourPlot x y, y x 1, x, 3, 3, y, 1, 5, ContourStyle Red, Blue, Axes True, AxesLabel x, y, Frame False 5 4 3 1 3 1 1 3 x y 1 y ax 1 a
8 GraphicsWithPlotFull.nb ContourPlotx y 1, x, 0, 4, y, 0, 4, Axes True, AxesLabel x, y, Frame False 4 3 1 ContourPlot a - Manipulate ContourPlotx y 1, y a x 1, x, 0, 4, y, 0, 4, Axes True, AxesLabel x, y, Frame False, a,, 4 3 1
GraphicsWithPlotFull.nb 9 Manipulate[(Plot ), {( ), ( ), ( )}] x y 1 0 1 1 aa x y 1. y a x 1 1 x 1 a x xd D=0 d Discriminant x y 1. y a x 1, x 4 4 a 3 a Solve d 0, a a 0, a 4 3 0 a 4 3-1 x y 8 y x 5 x 6
10 GraphicsWithPlotFull.nb ContourPlot x y 8, y x 5 x 6, x, 5, 3, y,, 6, Axes True, AxesLabel x, y, Frame False 6 4 4 x - x y 10 (1)y x ()y 3 x 10 (3)y x 8
GraphicsWithPlotFull.nb 11 ContourPlot x y 10, y x, y 3 x 10, y x 8, x, 5, 5, y, 5, 5, ContourStyle Red, Blue, Yellow, Green, Axes True, AxesLabel x, y, Frame False 4 4 4 4 y x y 3 x 10 Solve x y 10, y x, x, y x 1, y 3, x 3, y 1 Solve x y 10, y 3 x 10, x, y x 3, y 1, x 3, y 1 () Solve x y 10, y 3 x 10, x, y 1 x 3, y 1-3 A 3, 1 x y 5 Manipulate m (3, 1) y 1 m x 3
1 GraphicsWithPlotFull.nb Manipulate ContourPlot x^ y ^ 5, y 1 m x 3, x, 3, 5, y, 4, 4, Axes True, AxesLabel x, y, Frame False, m, 10, 10 4 4 c x^ y ^ 5; y =m(x - 3)+1 c. y m x 3 1 5 1 m 3 x x x 0 d Discriminant c. y m x 3 1, x 8 3 m m sol Solve d 0, m m 1, m y m x 3. sol y 3 x, y 3 x
GraphicsWithPlotFull.nb 13-4 y x ax y 4 (1)a ()4 a Manipulate a Manipulate ContourPlot x^ y ^ 4, y x^ a, x, 4, 4, y, 4, 4, Axes True, AxesLabel x, y, Frame False, a, 3, 5 4 4 4 x x y f x^ y ^ 4. x^ y a 4 a y y D D=0 d Discriminant f, y 17 4 a Solve d 0, a1 a 17 4 1 (0, ), (0, -) a=, -
14 GraphicsWithPlotFull.nb 4 a (0, ) (0, 17/4) ( ) a 17 4-5 x y 16 a y x 5 a a Manipulate Manipulate ContourPlot x^ y ^ 16, a y x^ 5 a, x, 10, 10, y, 10, 10, Axes True, AxesLabel x, y, Frame False, a, 100, 100 10 5 10 5 5 10 5 a x y c x^ y ^ 16. x^ a y 5 a 16 5 a a y y D D=0 d Discriminant c, y 64 0 a a
GraphicsWithPlotFull.nb 15 Solve d 0, a a 4, a 16 3(Graphics) Graphics Graphics Red, Circle 0, 0,, Green, Rectangle 0, 1, 1, 1, Yellow, Disk, Purple, Arrow 3, 1, 3, 1 Circle[{( x ), ( y )}, ( )] Rectangle[{(x ), (y )}, {(x ), (y )} Graphics Show g1 Plot Exp x, Exp ' 1 x 1 Exp 1, x, 0, ; g Graphics Red, Disk 1, E, 0.05; Show g1, g 7 6 5 4 3 1 0 x Π sin x 1
16 GraphicsWithPlotFull.nb sin x 1 eq Sin x 1 Sin x 1 Reduce eq, x C 1 Integers && x Π 5 Π Π C 1 x Π C 1 6 6 Π 6 x 5 Π 6 g1 Graphics Circle 0, 0, 1, 0, Pi; g Graphics Red, Circle 0, 0, 1, Pi 6, 5 Pi 6, Line 0, 0, Cos Pi 6, Sin 5 Pi 6, Line0, 0, Cos 5 Pi 6, Sin 5 Pi 6; Show g1, g, Axes True, AxesLabel x, y 1.0 0.8 0.6 0.4 0. 1.0 3-1 y x x x 1 g1 Plot x^ x, x, 3, ; g Graphics Opacity 0., Red, Rectangle, 3, 1, 10 ;
GraphicsWithPlotFull.nb 17 Show g1, g, AxesLabel x, y 10 8 6 4 3 1 1 x x=1, Mathematicay=a D=0 f x^ x y x x y f. y a a x x d Discriminant f. y a, x 4 1 a Solve d 0, a a 1 y=1 Plot x^ x, 1, x, 3,, PlotStyle Red, Green 7 6 5 4 3 3 1 x sol Solve f. y 1 0, x x 1, x 1
18 GraphicsWithPlotFull.nb sol 1 x 1 x=1 y x^ x. x 1 5 3- y x 3 x 3 x (-1, 0) 1 x y=f(x) f x x^3 x^ 3 x 3 x x x 3 (-1, 0) g x f' 1 x 1 f 1 4 1 x g1 Plot f x, g x, x,, 5 ; g Graphics Red, Disk1, 0, 0.1; Show g1, g 50 40 30 0 10 1 1 3 4 5 f(x) g(x) sol Solve f x g x, x x 1, x 1, x 4 x sol 3 x 4
GraphicsWithPlotFull.nb 19 f 4 0 g3 Graphics Red, Disk 4, 0, 0.1; Show g1, g, g3 50 40 30 0 10 1 1 3 4 5 3-3 y x 8 x 9 x -1 y eq1 y x^ 8 x 9 y 9 8 x x x x 1y y eq eq1. x x 1, y y 1 Simplify 1 1 x x y g1 Plot x^ 8 x 9, x^ 1 x 1, x, 4, 1 10 8 6 4 3.5 3.0.5.0 1.5 ( ) (Minimize[( ), ( )] )
0 GraphicsWithPlotFull.nb Minimize x^ 8 x 9, x 1, x Minimize x^ 1 x 1, x 3, x 3 g Graphics Yellow, Arrow, 1, 3, 1, Red, Arrow 3, 1, 3, 3 ; Show g1, g 10 8 6 4 3.5 3.0.5.0 1.5 3-4 0 x Π cos x 3 0 eq Cos x Sqrt 3 0; Reduce eq && 0 x Pi, x x 5 Π 7 Π x 6 6 g1 Graphics Circle 0, 0, 1 ; g Graphics Gray, Line 1.5, 1, 1.5, 1, Red, Line 0, 0, Cos Pi 6, Sin 5 Pi 6, Line0, 0, Cos 5 Pi 6, Sin 5 Pi 6;
GraphicsWithPlotFull.nb 1 Show g1, g, Axes True, AxesLabel x, y 1.0 0.5 1.5 1.0 0.5 0.5 1.0 1.5 x 0.5 3-5 0 x Π sin x Π 3 3 eq Sin x Pi 3 Sqrt 3 Cos Π 6 x 3 Reduce eq && 0 x Pi, x x Π Π 3 Π 5 Π x x x 3 3 y sin x Π 3, y 3 g1 Plot Sin x Pi 3, x, 0, Pi ; g Graphics Gray, Line0, Sqrt 3, Pi, Sqrt 3, Red, Disk Pi, Sqrt 3, 0.05, Disk Pi 3, Sqrt 3, 0.05, Disk 3 Pi, Sqrt 3, 0.05, Disk 5 Pi 3, Sqrt 3, 0.05; Show g1, g, AxesLabel x, y 1.0 0.5 1 3 4 5 6 0.5 1.0
GraphicsWithPlotFull.nb 4( ) y log 4 1 x 4 log 4 x f x Log 4, 1 x^4 Log 4, x ; Plot f x, x, 0, 5 4.0 3.5 3.0.5.0 1.5 1.0 Limit f x, x 0 Limit f x, x Infinity f(x) Minimize Minimize f x, x Log, x 1 Log 4 4-1 y x y x k k Manipulate
GraphicsWithPlotFull.nb 3 Manipulate Plotx^, x k, x, 5, 5, k, 100, 100 0 10 4 4 10 0 y f x^ y; f. y x k k x x d Discriminant f. y x k, x 4 1 k d>0 Reduce d 0, k k 1 d=01 Reduce d 0, k k 1 d<0 Reduce d 0, k k 1 4-3 x 3 6 x a 0a Manipulate
4 GraphicsWithPlotFull.nb Manipulate Plot x^3 6 x a, x, 3, 3, a, 10, 10 10 5 3 1 1 3 5 10 15 x 3 6 x a 0 y x 3 6 x a x x 3 6 x ay x 3 6 x, y a Manipulate Plot x^3 6 x, a, x, 3, 3, a, 5, 5 10 5 3 1 1 3 5 10 15 f x x 3 6 x f x x^3 6 x; f'(x)
GraphicsWithPlotFull.nb 5 Plot f' x, x,, 5 1 1 5 10 15 x sol Solve f' x 0, x x 1, x 1 x, f' x. sol 1, 0, 1, 0 f x. sol 4, 4 a 4, 4 a 1a 4, 4 4 a 4 3 4-3 I 0 Π sin x 3 cos x x Plot Abs Sin x Sqrt 3 Cos x, y 0 && 0 x Pi, x,, Pi 1, Filling 1 1.5 1.0 0.5
6 GraphicsWithPlotFull.nb 4-4 x f x t t t f x Integrate t^ t, t,, x x x 3 x3 3 Plot f x, x, 4, 4 5 4 4 5 f(x) f' x x x Plot f' x, x, 4, 5 15 10 5 4 4 x sol Solve f' x 0, x x 1, x x=-1 x=
GraphicsWithPlotFull.nb 7 f x. sol 11 6, 8 3 4-5 S x y 4 ContourPlot ContourPlot x^ ^ y ^ 4, x, 3, 3, y, 3, 3, Axes True, AxesLabel x, y, Frame False 3 1 3 1 1 3 1 y Reduce x^ ^ y ^ 4, y y 4 x x 4 y 4 x x 4
8 GraphicsWithPlotFull.nb Plot Sqrt 4 x^ x^4, x, 3, 3 1.5 1.0 0.5 3 x x Solve Sqrt 4 x^ x^4 0, x x, x 0, x - Integrate Sqrt 4 x^ x^4, x,, 3 3