Question

The paraboloid

* z* = 5 −

intersects the plane *x* = 4 in a parabola. Find
parametric equations in terms of *t* for the tangent line to
this parabola at the point

(4, 2, −23).

(Enter your answer as a comma-separated list of equations. Let
*x*, *y*, and *z* be in terms of
*t*.)

Answer #1

The paraboloid z = 5 − x − x2 − 2y2 intersects the plane x = 1
in a parabola. Find parametric equations in terms of t for the
tangent line to this parabola at the point (1, 4, −29). (Enter your
answer as a comma-separated list of equations. Let x, y, and z be
in terms of t.)

(1) The paraboloid z = 9 − x − x2 − 7y2 intersects the plane x =
1 in a parabola. Find parametric equations in terms of t for the
tangent line to this parabola at the point (1, 2, −21). (Enter your
answer as a comma-separated list of equations. Let x, y, and z be
in terms of t.)
(2)Find the first partial derivatives of the function.
(Sn = x1 +
2x2 + ... + nxn; i
= 1,...

Find equations of the following.
x2 − 3y2 + z2 + yz =
52, (7, 2, −5)
(a) the tangent plane
(b) parametric equations of the normal line to the given surface at
the specified point. (Enter your answer as a comma-separated list
of equations. Let x, y, and z be in
terms of t.)

The paraboloid z = 3x2 + 2y2 + 1 and the plane 2x – y + z = 4
intersect in a curve C. Find the points on C that have a maximum
and minimum distance from the origin.
The point on C is the maximum distance from the origin is (___ ,
____ , ____). The point on C is the minimum distance
from the origin is (____ , ____ , ____).
So for this question I get...

(a) Show that the parametric equations
x = x1 +
(x2 −
x1)t, y
= y1 +
(y2 −
y1)t
where
0 ≤ t ≤ 1,
describe (in words) the line segment that joins the points
P1(x1,
y1)
and
P2(x2,
y2).
(b) Find parametric equations to represent the line segment
from
(−1, 6) to (1, −2).
(Enter your answer as a comma-separated list of equations. Let
x and y be in terms of t.)

The
plane y+z=2 intersects the ‘funky’ cylinder x^2 + y^4 =17 in a
curve C.
A) Find a parametric equation of the tangent line to C at the
point (4,1,1)
B) How was the direction vector found in part A and how do you
know its the right direction?

Find a parametric representation for the surface.
The part of the sphere
x2 +
y2 + z2 =
16
that lies above the conez =
x2 + y2
. (Enter your answer as a comma-separated list of equations. Let
x, y, and z be in terms of u
and/or v.)
where z >
x2 + y2

Find a set of parametric equations for the tangent line to the
curve of intersection of the surfaces at the given point. (Enter
your answers as a comma-separated list of equations.)
z = x2 +
y2, z = 9 −
y, (3, −1, 10)

say that point (x, y, z) is the plane tangent to the
paraboloid z = x ^ 2 + 3y ^ 2 parallel to the plane z = x + y

Find the volume of the solid that lies under the paraboloid
z=2x2+2y2 above the xy-plane, and inside the
cylinder x2+y2=8y

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