Unit Tangent and Unit Normal Vectors Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Find the unit tangent vector and the unit normal vector for the curve with

(2) Find the unit tangent vector and the unit normal vector for the curve

(3) Find the unit tangent vector and the unit normal vector for the curve

(4) Find the length of the curve over the interval

(5) Find the length of the curve over the interval

(6) Find the length of the curve over the interval

(7) Find the curvature of the plane curve at the point .

(8) Find the curvature of the plane curve at the point .

(9) Express the vector function in terms of the arc length parameter measured from the point where in the direction of increasing

(10) Express the vector function in terms of the arc length parameter measured from the point where in the direction of increasing

(11) Find the unit tangent vector for which at the point where

(12) Given find so that

(13) Given find so that

(14) Find the length of the given curve described by the vector function



over the interval

(15) Determine so that the length of the given curve described by the vector function



has length over the interval

(16) Express the vector function in terms of the arc length parameter measured from the point where in the direction of increasing

(17) Determine so that the vector function written in terms of the arc length parameter measured form the point where in the direction of increasing is

(18) Given the vector function and find the unit tangent vector and the curvature at

(19) If is a smooth curve in described by the parametric equations and then the curvature is given by



Use this formula to find the curvature of the curve described by the parametric equations   and

(20) Find the point(s) where the ellipse has maximum curvature.

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Unit Tangent And Unit Normal Vectors Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
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