Question

6.) Let ~r(t) =< 3 cos t, -2 sin t > for 0 < t < pi. a) Sketch the curve. Make sure to pay attention to the parameter domain, and indicate the orientation of the curve on your graph. b) Compute vector tangent to the curve for t = pi/4, and sketch this vector on the graph.

Answer #1

So finally, the equation of tangent becomes-

y=(2x/3)-2√2 ..... And the tangent plotted on the same sketch where the ellipse is drawn..!!

2)Find the slope of the tangent line to the curve r = sin (O) +
cos (O) at O = pi / 4 (O means theta)
3)Find the unit tangent vector at t = 0 for the curve r (t) =
4sen (t) i + 3tj + cos (t) k
4)A uniform cable measuring 40 feet is hung from the top of a
building. The cable weighs 60 pounds. How much work in foot-pounds
is required to climb 10 feet...

Let C be a closed curve parametrized by r(t) = sin ti+cos tj
with 0 ≤ t ≤ 2π. Let F = yi − xj be a vector field.
(a) Evaluate the line integral xyds. C
(b) Find the circulation of F over C. (c) Find the flux of F
over C.

Consider the following vector function.
r(t) =
6t2, sin(t) − t cos(t), cos(t) + t sin(t)
, t > 0
(a) Find the unit tangent and unit normal vectors
T(t) and
N(t).
T(t)
=
N(t)
=
(b) Use this formula to find the curvature.
κ(t) =

Find the length of the curve
1) x=2sin t+2t, y=2cos t, 0≤t≤pi
2) x=6 cos t, y=6 sin t, 0≤t≤pi
3) x=7sin t- 7t cos t, y=7cos t+ 7 t sin t, 0≤t≤pi/4

Find a unit tangent vector to the curve r = 3 cos 3t
i + 3 sin 2t j at t =
π/6 .

6) please show steps and explanation.
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the area of the triangle
PQR.

Use a computer to graph the curve with the given vector
equation. Make sure you choose a parameter domain and view-points
that reveal the true nature of the curve
r(t)=< te^t, e^-t, t>
r(t) = < cos(8cos t) sint t , sin(8cos t) sin t, cos t
>
Please I need to graph in MATLAB these are problems for Stewart
Calculus 8th edition.
I don't not how to use matlab please I need the commands. Thank
you for your help!

Find r(t) for the given
conditions.
r''(t) = −7
cos(t)j − 3
sin(t)k, r'(0)
=
3k, r(0)
= 7j

Given r(t)=sin(t)i+cos(t)j−ln(cos(t))k, find the unit normal
vector N(t) evaluated at t=0,N(0).

Evaluate the integral.
pi/2
3
sin2(t) cos(t)
i + 5 sin(t)
cos4(t) j + 4
sin(t) cos(t)
k dt
0

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 19 minutes ago

asked 22 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago