Question

Evaluate (if possible) the vector-valued function at each given
value of *t*. (If you need to use Δ*t*, enter
Deltat.)

**r**(t) = 1/2t^{2}**i** − (t
− 9)**j**

Evaluate (if possible) the vector-valued function at each given
value of *t*. (If an answer does not exist, enter DNE.)

**r**(t) = cos(t)**i** + 9
sin(t)**j**

Answer #1

Find the vectors T and N and
the binormal vector B = T ⨯
N, for the vector-valued function
r(t) at the given value of
t.
r(t) = 6 cos(2t)i + 6
sin(2t)j +
tk, t0 =
pi/4
find:
T(pi/4)=
N(pi/4)=
B(pi/4)=

Given that the acceleration vector is a ( t ) = (−9 cos( 3t ) )
i + ( −9 sin( 3t ) ) j + ( −5 t ) k, the initial velocity is v ( 0
) = i + k, and the initial position vector is r ( 0 ) = i +j + k,
compute: the velocity vector and position vector.

Given that the acceleration vector is a(t)=(-9 cos(3t))i+(-9
sin(3t))j+(-5t)k, the initial velocity is v(0)=i+k, and the initial
position vector is r(0)=i+j+k, compute:
A. The velocity vector v(t)
B. The position vector r(t)

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).

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 the velocity, acceleration, and speed of a particle with
the given position function.
(a) r(t) = e^t cos(t)i+e^t
sin(t)j+ te^tk, t = 0
(b) r(t) = 〈t^5 ,sin(t)+ t ^ cos(t),cos(t)+ t^2 sin(t)〉, t =
1

Solve the initial value problems in Exercises 11–20 for r as a
vector function of t.
15. Differential equation: dr/dt = (tan t)i +(cos(t /2 ))j -
(sec(2t))k
Initial condition: r(0) = 3i - 2j + k

Evaluate the surface integral S F · dS for the given vector
field F and the oriented surface S. In other words, find the flux
of F across S. For closed surfaces, use the positive (outward)
orientation. F(x, y, z) = y i − x j + z2 k S is the helicoid (with
upward orientation) with vector equation r(u, v) = u cos v i + u
sin v j + v k, 0 ≤ u ≤ 5, 0...

Given r(t) = (et cos(t) )i + (et sin(t) )j
+ 2k. Find
(i) unit tangent vector T.
(ii) principal unit normal vector N.

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) =

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