Question

- Describe the surface 9
*x*^{2}+ 4*y*^{2}+*z*^{2}= 1

Answer #1

please comments if you have any problems

1. a) Sketch the surface. 9x2 +
4y2 + z2
= 36. Identify the surface.
b) Sketch the surface. z = 4 −
y2. Identify the surface.
c) Sketch the surface. y =
5z2 −
5x2. Identify the surface.
d) Sketch the surface. 6x2 −
y2 + z2 =
0 . Identify the surface.
e) Sketch the surface. 6x2 +
4y2 + z = 0 .
Identify the surface.

Write the equations in cylindrical coordinates.
9x2 − 3x + 9y2 + z2 = 9
// I keep getting z^2=9-3r(3r-cos (theta))

Write the equations in cylindrical coordinates.
(a) 8x2 − 7x + 8y2
+ z2 = 1
(b) z = 4x2 − 4y2

Calculate ∫ ∫S f(x,y,z)dS for the given surface and function.
x2+y2+z2=144, 6≤z≤12; f(x,y,z)=z2(x2+y2+z2)−1.

Find the point on the surface (x-3)2 +
(y-2)2 + z2 =1 that is closest to the
origin.

Find the surface area of the cone x2 + y2
= z2 that lies inside the sphere x2 +
y2 + z2 = 6z by taking integrals.

(1) Sketch the given surfaces ( for Question (a) and (b) graph
x=0, y=0 and z=2 traces)
(a) x2-4y2=z
(b) y2-4x2-z2=4
(2) state the type of the quadric surface and describe the trace
obtained by intersecting with the given plane.
(x/2)2+(y/5)2-5z2=1, x=0

Evaluate the area of the part of the conical surface
x2 + y2 = z2 bounded below by the
sphere x2 + y2 + z2 = 4 and above
by the plane 2x + y + 10z = 20. Derive the final form of the
integral.

Compute the surface integral over the given oriented
surface:
F=〈0,9,x2〉F=〈0,9,x2〉 , hemisphere
x2+y2+z2=4x2+y2+z2=4, z≥0z≥0 , outward-pointing
normal

Find the area of the surface. The part of the sphere x2 + y2 +
z2 = 64 that lies above the plane z = 3.

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