Question

x=2−t, y=2t+1; −1≤t≤1

(a) Sketch the parametrized curve using any method, but you must explain your thinking in clear sentences, or show mathematical work. Pay attention to the given domain. (b) Choose one of (i) or (ii) below – only one will be graded. i. Set up and solve an integral for the arc length of this curve OR ii. Calculate the equation of the tangent line to this curve at some point (tell the reader which point you chose!) using methods of 7.2

Answer #1

Let C be the curve parametrized by r(t)=(t2+2)i+(1+t)j+2t^2k,
with 0≤t≤. Consider the conservative vector field
F=yz2i+xz2j+2xyzk, Calculate ∫CF⋅dr

1. A plane curve has been parametrized with the following
vector-valued function, r(t) = (t + 2)i + (-2t2 + t + 1)j a.
Carefully make 2 sketches of the plane curve over the interval . (5
pts) b. Compute the velocity and acceleration vectors, v(t) and
a(t). (6 pts) c. On the 1st graph, sketch the position, velocity
and acceleration vectors at t=-1. (5 pts) d. Compute the unit
tangent and principal unit normal vectors, T and N at...

A space curve C is parametrically parametrically defined by
x(t)=e^t^(2) −10,
y(t)=2t^(3/2) +10,
z(t)=−π,
t∈[0,+∞).
(a) What is the vector representation r⃗(t) for C ?
(b) Is C a smooth curve? Justify your answer.
(c) Find a unit tangent vector to C .
(d) Let the vector-valued function v⃗ be defined by
v⃗(t)=dr⃗(t)/dt
Evaluate the following indefinite integral
∫(v⃗(t)×i^)dt. (cross product)

1. y=∫upper bound is sqrt(x) lower bound is 1,
cos(2t)/t^9 dt
using the appropriate form of the Fundamental Theorem of
Calculus.
y′ =
2. Use part I of the Fundamental Theorem of Calculus to find the
derivative of
F(x)=∫upper bound is 5 lower bound is
x, tan(t^4)dt
F′(x) =
3. If h(x)=∫upper bound is 3/x and lower
bound is 2, 9arctan t dt , then
h′(x)=
4. Consider the function f(x) = {x if x<1, 1/x if x is >_...

2. SECURING THE WORKFORCE Diversity management in
X-tech, a Japanese organisation
This case is intended to be used as a basis for class discussion
rather than as an illustration of the effective or ineffective
handling of an administrative situation. The name of the company is
disguised.
INTRODUCTION
In light of demographic concerns, in 2012, the Japanese
government initiated an effort to change the work environment in
order to secure the workforce of the future. Japan is world
renowned for its...

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