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Chapter 11: Vector Functions

Expert-verified
Calculus
Pages: 851 - 902
Calculus

Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Illustration

290 Questions for Chapter 11: Vector Functions

  1. Problem Zero: Read the section and make your own summary of the material.

    Found on Page 897

  2. True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

    Found on Page 859

  3. Fillintheblankstocompleteeachofthefollowingtheoremstatements:Thederivativeofavectorfunctionr(t)isgivenbyr'(t)=limh→0

    Found on Page 900

  4. Unit vectors: If v is a nonzero vector, explain why v|v| is a unit vector.

    Found on Page 879

  5. Projecting one vector onto another: Show that the formula for the projection of a vector v onto a nonzero vector u is given byprojuv=u.v|u|,whereu≠0.

    Found on Page 897

  6. Sketching vector functions: Sketch the following vector functions.

    Found on Page 901

  7. Let r(t)=xt,yt,t∈[a,∞), be a vector-valued function, where a is a real number. Explain why the graph of r may or may not be contained in a circle centered at the origin. (Hint: Graph the functions r1t=1t,1tand r2t=t,t,both with domain [1,∞)

    Found on Page 859

  8. Given a twice-differentiable vector-valued function r(t), why does the principal unit normal vector N(t) point into the curve?

    Found on Page 879

  9. Velocity and acceleration vectors: Find the velocity and acceleration vectors for the given vector functions.

    Found on Page 901

  10. Statewhatitmeansforavectorfunctionr(t)=x(t),y(t),z(t)tobeintegrable

    Found on Page 871

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