## 10 Reputation

9 years, 112 days

## A question about create a animation...

Question (A)

The surface z=f(x,y)=5/(1+x^2+y^2) is a hill. A bug walks along the path with x(t)=2+3cos(t) and y(t)=-1+2sin(t)

and z(t) is on the surface (0≤t≤2pi).

Plot the surface z for -4≤x≤7, -4≤y≤4 and includethe path (in thick black) of the bug on the surface.

(this will require 2 graphing commands plus a display 3d. Think spacecurve for the bug's path.)

Animate a solid...

## a problem about the surface...

SURF is the surface z=2x^2+y^2 for x=0 .. 2, y=0 ..4 and view= -1 ..16.

L is a straight line laser beam x=7-2t, y=t, z=4t-1 which hits SURF at the point P=(1, 3, 11).

Graph SURF, the laser path in red (t=0 to 3), the normal vector at P in black, and the reflected path in green.

Include the equations of the normal vector and the reflected path.

## a question about the surface...

The surface z=f(x,y)=5/(1+x^2+y^2) is a hill. A bug walks along the path with x(t)=2+3cos(t) and y(t)=-1+2sin(t)

and z(t) is on the surface (0≤t≤2pi).

Plot the surface z for -4≤x≤7, -4≤y≤4 and includethe path (in thick black) of the bug on the surface.

(this will require 2 graphing commands plus a display 3d. Think spacecurve for the bug's path.)

## A problem about plot the part of the sur...

Maple

plot part of the surface f(x,y)=10-x^2-3y^2:

plot3d(10-x^2-3y^2, x=-1 .. 4, y=1 .. 2, view=0 .. 11, axes= normal); (press enter)

Determine the normal vector and the equation of the tangent plane at the point (2,1,3) on the surface.

Display the surface , a black vector and the tangent plane, and give the equation for each of them

label the normal vector and the tangent plane, and give the equation for each of them

## a question about osculating circle...

Maple 15

In 2D, graph a blue ellipse x(t)=3cos(t), y(t)=2sin(t) for 0≤t≤2∏. For t=0.5 graph a green tangent line to the ellipse and a red osculating circle. Also, give the curvature, the equation of the tangent line and the center of the osculating circle

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