Problem 1
Consider the curve parameterized by the vector function
(a). Find a Surface on Which the Parameterized Curve Lives and Sketch the Curve and the Surface in the Space below
The curve is a helix which lies on the cone .
(b). Find . You Must Simplify Your Answer to Get Credit for This Problem there Should Be no Sines or Cosines in Your Answer
(c). Find , where is Arc Length
(d). Find
(e). Find
(f). Find
(g). Deduce from the above Answers what is (hint: Use the Decomposition of Acceleration into Normal and Tangential components)
(h). Find the Equation of the Osculating Plane at
Problem 2
Suppose that is a vector valued function with and where and are some constants. Compute the quantity . Your answer should be expressed solely in terms of and (hint: it helps to draw a picture of the vectors , , and for some fixed value of ).
Problem 3
Let , be a parameterized curve. Re-parameterize the curve by arc length beginning at the point
and going in the positive direction. Geometrically describe this curve.
The curve parameterized by arc length represents a curve passing through in the direction of