kadai-2.nb
1
Plot@
82 Sin@xD + x ^ 3 − x, 2 x ^ 2<,
8x, 0, 3<
D
20
15
10
5
0.5
1
1.5
Graphics
FindRoot@
2 Sin@xD + x ^ 3 − x == 2 x ^ 2,
8x, 2<
D
8x → 2.07536<
FindRoot@
2 Sin@xD + x ^ 3 − x == 2 x ^ 2,
8x, 1<
D
8x → 0.636321<
2
2.5
3
kadai-2.nb
2
Show@
Graphics@
8
[email protected], Rectangle@8−1.2, −1.2<, 81.2, 1.2<D<,
[email protected], Circle@80, 0<, 1D<,
Table@
[email protected], Hue@i ê 12D,
Line@880, 0<, 8Cos@2 Pi ∗ i ê 12D, Sin@2 Pi ∗ i ê 12D< < D<, 8i, 0, 12<D,
[email protected], Point@80, 0<D<,
[email protected],
Table@8Hue@1 − i ê 12D, Point@8Cos@2 ∗ Pi ∗ i ê 12D, Sin@2 ∗ Pi ∗ i ê 12D<D<, 8i, 0, 12<D<
D
<
, AspectRatio → AutomaticD
Graphics
cycloid@t_D := 8t − Sin@tD, 1 − Cos@tD<;
kadai-2.nb
frames = 30;
locus = Table@cycloid@tD, 8t, 0, 2 Pi, 2 Pi ê Hframes − 1L<D;
Do@
Show@
t = i ∗ 2 Pi ê Hframes − 1L;
Graphics@
8
[email protected], Disk@8t, 1<, 1D<,
Circle@8t, 1<, 1D,
Line@88−1, 0<, 87, 0<<D,
8
AbsoluteThickness@2D,
Line@88t, 1<, locus@@i + 1DD<D
<,
8
AbsolutePointSize@3D,
Map@Point, Take@locus, i + 1DD
<
<
D,
AspectRatio → Automatic,
PlotRange → 88−1.5, 7.5<, 8−0.2, 2.2<<
D,
8i, 0, frames − 1<
D
3
kadai-2.nb
4
f@x_, y_D := Hx ^ 2 + 3 y ^ 2L E ^ H1 − x ^ 2 − y ^ 2L
Plot3D@
f@x, yD,
8x, −2, 2<,
8y, −2, 2<,
PlotPoints → 30,
AxesEdge → 8Automatic, 81, −1<, 81, 1<<,
AxesLabel → 8"x", "y", None<
D
3
2
1
0
2
1
-2
0
-1
-1
0
x
1
2 -2
SurfaceGraphics
y
kadai-2.nb
5
ContourPlot@
f@x, yD,
8x, −2, 2<,
8y, −2.5, 2.5<,
PlotPoints → 50,
ColorFunction → HHue@1 − # ê 2D &L
D
2
1
0
-1
-2
-2
-1
0
1
2
ContourGraphics
f@x_, y_D := If@x ^ 2 + y ^ 2 ≤ 1, Sin@x yD, 0D
Plot3D@
f@x, yD,
8x, −1.5, 1.5<,
8y, −1.5, 1.5<,
PlotPoints → 50,
AxesLabel → 8"x", "y", "z"<
D
0.4
0.2
z
0
-0.2
-0.4
1
0
-1
0
-1
x
1
SurfaceGraphics
y