ENGR 1405 Engineering Mathematics 1

Faculty of Engineering and Applied Science
2000 Fall

Problem Set 9
Questions

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Note:   if you see symbols like ³ or Þ in various places, then your browser is not reading the style sheet for this Web page properly (or the Symbol font is not installed on your computer).   The translation is:

k   =   k   (kappa)

q   =   q   (theta)

1. For the curve defined parametrically by , determine

   1. the tangent vector , and
   2. the element of arc length "ds".

   Also:

   3. Eliminate the parameter   t   to find a Cartesian equation of this curve.

2. For the curve defined parametrically by , determine

   1. the tangent vector , and
   2. the element of arc length "ds".

3. For the curve defined parametrically by , determine

   1. the tangent vector , and
   2. the element of arc length "ds".

4. For the curve whose Cartesian equation is

   x^2/3 + y^2/3 = 1

   1. Write down a simple parametric form for this curve (using trigonometric functions) and find
   2. the tangent vector , and
   3. the element of arc length "ds".

5. For the curve of intersection of the plane     and the elliptic cylinder     defined parametrically by

   

   find:

   1. the tangent vector , and
   2. the element of arc length "ds".

6. For the curve defined parametrically by , determine

   1. the tangent vector ,
   2. the element of arc length "ds", and
   3. the length of the curve from

7. For the curve defined parametrically by , determine

   1. the tangent vector ,
   2. the element of arc length "ds" , and
   3. the length of the curve from

   Also:

   4. Eliminate the parameter   q   to find a Cartesian equation of this curve.
      [Let   q   be any real number.]
   5. Hence sketch this curve.

8. For the curve defined parametrically by , determine

   1. the tangent vector ,
   2. the element of arc length "ds" , and
   3. the length of the curve from

   4. What type of curve is r(p)?.

9. Determine the unit tangent vector, , the unit principal normal vector, , and the curvature k for the curve defined parametrically by .

   Also:

   Eliminate the parameter   t   to find a Cartesian equation of this curve.
   [Let   t   be any real number.]

   Hence sketch this curve.

10. Determine the unit tangent vector, , the unit principal normal vector, , and the curvature k for the curve defined parametrically by .

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Created 1999 12 01 and modified 2000 11 29 by Dr. G.H. George