Question

[6]
The object is on move along the curve (y = x^2) & (z = x^3)
with a vertical speed, which is constant (dz/dt = 2) find the
acceleration and velocity when the object is at point P (2, 4, 8)

[7] (a) A plane (z = 2+x) which does intersects the cone (z^2
= x^2 + y^2) in a parabola. Parameterize the parabola using (t =
y). [Find f(t)] & [h(t)] where as [r = f(t)i + (t) j + h(t)k]
everything representing the Parabola

(b) where as, [r = (t) i + (t^2/2) j +(t^2)k, find the
curvature, the unit which is tangent and the normal unit

Answer #1

Let w(x,y,z) = x^2+y^2+z^2 where x=sin(8t), y=cos(8t) , z=
e^t
Calculate dw/dt by first finding dx/dt, dy/dt, and dz/dt and using
the chain rule
dx/dt =
dy/dt=
dz/dt=
now using the chain rule calculate
dw/dt 0=

Let y = x 2 + 3 be a curve in the plane.
(a) Give a vector-valued function ~r(t) for the curve y = x 2 +
3.
(b) Find the curvature (κ) of ~r(t) at the point (0, 3). [Hint:
do not try to find the entire function for κ and then plug in t =
0. Instead, find |~v(0)| and dT~ dt (0) so that κ(0) = 1 |~v(0)|
dT~ dt (0) .]
(c) Find the center and...

Evaluate Integral (subscript c) z dx + y dy − x dz, where the
curve C is given by c(t) = t i + sin t j + cost k for 0 ≤ t ≤
π.

The paraboloid
z = 5 − x −
x2 −
2y2
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.)

Use the Chain Rule to find dz/dt. (Enter your
answer only in terms of t.)
z=sqrt(1+x^2+y^2), x=ln(t), y=cos(t)
dz/dt=

1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and S(x, y, z) =
(2y − z, x − z, y + 3x). Use matrices to find the composition S ◦
T.
2. Find an equation of the tangent plane to the graph of x 2 − y
2 − 3z 2 = 5 at (6, 2, 3).
3. Find the critical points of f(x, y) = (x 2 + y 2 )e −y...

Compute the line integral of f(x, y, z) = x 2 + y 2 −
cos(z) over the following paths:
(a) the line segment from (0, 0, 0) to (3, 4, 5)
(b) the helical path → r (t) = cos(t) i + sin(t) j + t k from
(1, 0, 0) to (1, 0, 2π)

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,...

1. f(x, y, z) = 2x-1 − 3xyz2 + 2z/
x4
2. f(s, t) = e-bst − a ln(s/t) {NOTE: it is
-bst2 }
Find the first and second order partial derivatives for question
1 and 2.
3. Let z = 4exy − 4/y and x =
2t3 , y = 8/t
Find dz/dt using the chain rule for question 3.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 6 minutes ago

asked 39 minutes ago

asked 40 minutes ago

asked 40 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago