APPM 2350 - Recitation
Fall 2016
Worksheet 3
10.6 - Cylinders and Quadratic Surfaces
1. Describe/give an example of the following:
(a) parabolic cylinder:
(b) quadric surface:
(c) elliptic paraboloid:
(d) hyperbolic paraboloid:
2. Identify and sketch the following:
(a) y = z 2
(b) x2 + z 2 = 3
(c) 4x2 + y 2 +
z2
7
=1
(d) x2 /9 + y 2 /4 − z 2 = 0
Worksheet 3 continued on next page. . .
APPM 2350 - Recitation
3. Sketch the region bounded by the surfaces x =
Fall 2016
p
y 2 + z 2 and y 2 + z 2 = 1 for 1 ≤ x ≤ 2.
4. Show that the curve of the intersection of the surfaces x2 +2y 2 −z 2 +3x = 1 and 2x2 +4y 2 −2z 2 −5y = 0
lies in a plane.
10.7 - Vector Functions and Space Curves
1. A vector-valued function is any function r :
→
, that is,
, and outputs a
any function that inputs a
2. If r(t) = hf (t), g(t), h(t)i, then limt→a r(t) =
.
, provided that
.
3. A vector function r is continuous at a if
.
4. At what points does the helix r(t) = hsin t, cos t, ti intersect the sphere x2 + y 2 + z 2 = 10?
5. Find a vector function that represents the curve of the intersection of the paraboloid z = 4x2 + y 2 and
the parabolic cylinder y = x2 .
√
6. Find the parametric equations for the tangent line to the curve x = ln t, y = 2 t, z = t2 at the point
(0, 2, 1).

, , y x z = F r , 2 sin , 2 z y z e e y y xz xye = +

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