Question

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=

Answer #1

we have

now,

by the chain rules,

......................i)

put t = 0,

....................ii)

Use the Chain Rule to find dw/dt.
w = ln
x2 + y2 + z2
, x = 9 sin(t), y
= 4 cos(t), z = 5 tan(t)
dw
dt
=

Find dw/dt using the appropriate chain rule for w=x^2+y^2+z^2
where x=8tsin(s), y=8tcos(s) and z=5st^2

it is known that W=x2y+y+xz where x=cos A, y=sin A,
and z=A2. find DW/DA and calculate the value of
A=1/3

Evaluate C (y + 6 sin(x)) dx + (z2 + 2 cos(y)) dy + x3 dz where
C is the curve r(t) = sin(t), cos(t), sin(2t) , 0 ≤ t ≤ 2π. (Hint:
Observe that C lies on the surface z = 2xy.) C F · dr =

1.express dw/dt as a function of t, both by using the Chain Rule
and by expressing w in terms of t and differentiating directly with
respect to t. Then evaluate dw/dt at the given value of t.
a)w= -6x^2-10x^2 , x=cos t,y=sint, t=pi/4
b)w=4x^2y-4y^2x, x=cost y=sint, --> express n terms of t
2.Find the linearization L(x,y) of the function (x,y)=e^x
cos(9y) at points (0,0) and (0,pi/2)

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=

letw be the region bounded by z=1-y^2,y=x^2 and the plane
z=0.Calculate the volume of W in the order of dz dy dx.

find dx/dx and dz/dy
z^3 y^4 - x^2 cos(2y-4z)=4z

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.

1. Solve the following differential equations.
(a) dy/dt +(1/t)y = cos(t) +(sin(t)/t) , y(2pie) = 1
(b)dy/dx = (2x + xy) / (y^2 + 1)
(c) dy/dx=(2xy^2 +1) / (2x^3y)
(d) dy/dx = y-x-1+(xiy+2) ^(-1)
2. A hollow sphere has a diameter of 8 ft. and is filled half way
with water. A circular hole (with a radius of 0.5 in.) is opened at
the bottom of the sphere. How long will it take for the sphere to
become empty?...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 17 minutes ago

asked 25 minutes ago

asked 31 minutes ago

asked 31 minutes ago

asked 36 minutes ago

asked 43 minutes ago

asked 51 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago