GraphicsWithPlotFull.nb Plot[{( 1), ( ),...}, {( ), ( ), ( )}] Plot Plot Cos x Sin x, x, 5 Π, 5 Π, AxesLabel x, y x 1 Plot AxesLabel

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1 1(Plot) f x x x 1 1 x x ( )[( 1)_, ( )_, ( 3)_,...]=( ) Plot Plot f x, x, 5, Plot[( ), {( ), ( ), ( )}] D g x x 3 x 3 Plot f x, g x, x, 10,

2 GraphicsWithPlotFull.nb Plot[{( 1), ( ),...}, {( ), ( ), ( )}] Plot Plot Cos x Sin x, x, 5 Π, 5 Π, AxesLabel x, y 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 PlotStyle->{Green, Red}

3 GraphicsWithPlotFull.nb 3 Plot x, Log x, x, 4, 4, PlotStyle Dashed, Thick PlotStyle {Dashed, Thick} Plot Sin x x, Sin x x, x, 4, 4, Filling Filling {1 {}} Mathematica 1-1 f x Exp x Exp[x] f x Exp x x

4 4 GraphicsWithPlotFull.nb Plot f x, x, 10, 10, AxesLabel x, y 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

5 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 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

6 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 (ContourPlot Manipulate) ycontourplot ContourPlot x y 1, x y, x y 3, x y 4, x,.,., y,.,

7 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 x y 1 y ax 1 a

8 8 GraphicsWithPlotFull.nb ContourPlotx y 1, x, 0, 4, y, 0, 4, Axes True, AxesLabel x, y, Frame False 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

9 GraphicsWithPlotFull.nb 9 Manipulate[(Plot ), {( ), ( ), ( )}] x y 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 a x y 8 y x 5 x 6

10 10 GraphicsWithPlotFull.nb ContourPlot x y 8, y x 5 x 6, x, 5, 3, y,, 6, Axes True, AxesLabel x, y, Frame False x - x y 10 (1)y x ()y 3 x 10 (3)y x 8

11 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 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

12 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, c x^ y ^ 5; y =m(x - 3)+1 c. y m x 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

13 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, 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 (0, ), (0, -) a=, -

14 14 GraphicsWithPlotFull.nb 4 a (0, ) (0, 17/4) ( ) a 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, 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

15 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 x Π sin x 1

16 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 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 y x x x 1 g1 Plot x^ x, x, 3, ; g Graphics Opacity 0., Red, Rectangle, 3, 1, 10 ;

17 GraphicsWithPlotFull.nb 17 Show g1, g, AxesLabel x, y 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 x sol Solve f. y 1 0, x x 1, x 1

18 18 GraphicsWithPlotFull.nb sol 1 x 1 x=1 y x^ x. x 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 x g1 Plot f x, g x, x,, 5 ; g Graphics Red, Disk1, 0, 0.1; Show g1, g f(x) g(x) sol Solve f x g x, x x 1, x 1, x 4 x sol 3 x 4

19 GraphicsWithPlotFull.nb 19 f 4 0 g3 Graphics Red, Disk 4, 0, 0.1; Show g1, g, g 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, ( ) (Minimize[( ), ( )] )

20 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 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;

21 GraphicsWithPlotFull.nb 1 Show g1, g, Axes True, AxesLabel x, y x 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

22 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, Limit f x, x 0 Limit f x, x Infinity f(x) Minimize Minimize f x, x Log, x 1 Log y x y x k k Manipulate

23 GraphicsWithPlotFull.nb 3 Manipulate Plotx^, x k, x, 5, 5, k, 100, 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 x 3 6 x a 0a Manipulate

24 4 GraphicsWithPlotFull.nb Manipulate Plot x^3 6 x a, x, 3, 3, a, 10, 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, f x x 3 6 x f x x^3 6 x; f'(x)

25 GraphicsWithPlotFull.nb 5 Plot f' x, x,, 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 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

26 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, f(x) f' x x x Plot f' x, x, 4, x sol Solve f' x 0, x x 1, x x=-1 x=

27 GraphicsWithPlotFull.nb 7 f x. sol 11 6, S x y 4 ContourPlot ContourPlot x^ ^ y ^ 4, x, 3, 3, y, 3, 3, Axes True, AxesLabel x, y, Frame False y Reduce x^ ^ y ^ 4, y y 4 x x 4 y 4 x x 4

28 8 GraphicsWithPlotFull.nb Plot Sqrt 4 x^ x^4, x, 3, x x Solve Sqrt 4 x^ x^4 0, x x, x 0, x - Integrate Sqrt 4 x^ x^4, x,, 3 3