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This is the Exam of Calculus Indefinite Integrals, Limits, Explanation, Curve Parametrized, Involve the Variables etc. Key important points are: Midpoint Rule, Indefinite Integrals, Methods, Approximate, Large, Choose, Accurate, Boxes, Trigonometric Substitution, Error Bound
Typology: Exams
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Midterm 1 June 1, 2005, 8:30 – 9:20 am
Last Name (please print): _________________________________________
First Name (please print): _________________________________________
Student Number: _________________________________________
Signature: _________________________________________
Instructions:
a) Suppose that M is the midpoint of the segment AB in space and that P is another point. Show that 1 ( 2
. [4 marks]
b) Suppose that a^ K^ and b are two unit vectors. Show that
a + b
is perpendicular to a − b. [4 marks]
a) Find the equation of the line that is tangent to its position vector and that is parallel to the line: 1 2 2
x − (^) = y = z + (^1). [6 marks]
b) Find the curvature of curve κ for t ≥ 0.
( Hint: 1 |^ '( )^ ''( ) | 3 | '( ) |
dT dT r t r t ds v dt r t
K ).^ [4 marks]