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Midterm

# ME201 me201mw06qExam

Department
Mechanical Engineering
Course Code
ME201
Professor
All
Study Guide
Midterm

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ME 201 ADVANCED CALCULUS
8 February 2006
Midterm Examination R. Culham
This is a two-hour, closed-book examination, where you are permitted to use:
Schaum’s - Mathematical Handbook of Formulas and Tables
one 8.5 in.×11 in. crib sheet. (one side)
There are 6 questions to be answered. Read the questions very carefully.
Clearly state all assumptions.
It is your responsibility to write clearly and legibly.
Reduce all equations to their simplest possible form.
Question 1 (11 marks)
For the curve given by
~
R(t) = ˆ
i(2 ln t)ˆ
j 1
t+t!ˆ
k
ﬁnd:
i) velocity and acceleration vectors
ii) the angle (radians) between the velocity and acceleration vectors at t= 1
iii) the unit tangent vector
iv) the principal unit normal vector
v) the length of the curve over the interval 1t2
Question 2 (7 marks)
Find the curvature of the path
~
R(t) = ˆ
i(etcos t) + ˆ
j(etsin t) + ˆ
k(et)
when t= 0.
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