Name: _
Exam #1
Math 1D
Form A
PLEASE TURN OFF ALL CELL PHONES AND PAGERS NOW. A 20% EXAM
PENALTY APPLIES IF YOUR CELL PHONE RINGS OR VIBRATES
DIRECTIONS: PLEASE READ THE DIRECTIONS BELOW CAREFULLY TO
AVOID SIGNIFICANT POINTS DEDUCTIONS.
1. Read all quest

Public health officials perplexed by vaccination skeptics
Published March 03, 2015 Associated Press
Certain that they are right, struggling to find ways to get their message across, public health officials are
exasperated by their inability to persuade mo

Problem 3
Use the helix:
r (t)=<a cos t, a sin t, t>, where 0 a 4 (a is a constant), to answer each question
below. SHOW ALL WORK.
(Debug) In[1]:=
r[t_] := a * Cos[t], a * Sin[t], t
A) Compute the velocity vector
(Debug) In[2]:=
(Debug) Out[2]=
v[t] = r

Curvature and the Unit Tangent Vector
Problem 1
Let's check that the formulas work for a circle parameterized by
r (t)=<R cos t, R sin t> (R>0). Compute the
curvature using either formula above and verify that you get 1/R for the curvature. Show work.
At

Properes of the Principal Unit Normal Vector
Problem 4
(Debug) In[1]:=
r[t_] := R * Cos[t], R * Sin[t], 0
A) Compute the principal unit normal vector to the curve in Problem 1 and verify that it is orthogonal to
the unit tangent vector (show the dot produ

Problem 9
Execute the command below to view the TNB Frame for the helix curve
r (t)=<2 cos t, 2 sin t, t>, 0 t
2 (Place the cursor at the end of the last line in the command group and press shift + return). Watch
how the principal unit normal N changes

Problem 5
The osculating circle at a point P on a smooth curve
r (t) is a circle in the plane containing the unit
normal and the unit tangent vectors and whose center is along the line through P with direction vector
N(t) and with radius, R = 1/, where i

Problem 8
Execute the command group below to generate the TNB frame for the curve
r (t)=<R cos t, R sin t>
(R>0). Put your cursor at the end of the last line of commands and press shift + return. Move the slider
and watch the three vectors move as you mo

Problem 7
Compute the unit binormal vector for each curve below. Show work in each case.
A)
r (t)=<R cos t, R sin t> (R>0)
(Debug) In[32]:=
r[t_] := R * Cos[t], R * Sin[t], 0
(Debug) In[33]:=
mag[vector_] :=
(Debug) In[35]:=
n[t_] := FullSimplify
vector.

Problem 10
Use your work from earlier in this exam to find the unit binormal vector at the point where t = 13/6 on
the helix
r (t)=<2 cos t, 2sin t, t> (this is the helix shown in Problem #9). The unit binormal vector is
normal to the osculating plane th

The Binormal Vector and the TNB Frame
Problem 6
Assuming nonzero vectors above,
a unit vector.
B(t) = T (t) N(t) explain why the cross product T N results in
Explanation: Because the binormal vector, B is defined to be the cross product of the unit tang

PROGRAMS AND MAJORS
Computer Information
Management
Local Area Networks: Cisco
Upon completion of the local area networks: Cisco program,
students will be able to
School of Business Sciences
Apply computing techniques to solve common business
problems,