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Chapter 11: Q.56 (page 873)

r1

Short Answer

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Most popular questions from this chapter

Let r(t)=xt,yt,t鈭�[a,鈭�), 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 摆1,鈭�).)

In Exercises 19鈥�21 sketch the graph of a vector-valued function r(t)=x(t),y(t) with the specified properties. Be sure to indicate the direction of increasing values oft.

Domainlocalid="1649578783745" t鈮�0,r0=1,0,r2=0,-1,limt鈫�鈭�x(t)=-2,andlimt鈫�鈭�y(t)=-3.

Given a twice-differentiable vector-valued function r(t), what is the definition of the principal unit normal vector N(t)?

Findthederivativeofthevector-valuedfunctionr(t)=t2i鈭�6t2j,t>0,andshowthatthederivativeatanypointt0isascalarmultipleofthederivativeatanyotherpoint.Whatdoesthispropertysayaboutthegraphofr?Usethatinformationtosketchthegraphofr.

Find parametric equations for each of the vector-valued functions in Exercises 26鈥�34, and sketch the graphs of the functions, indicating the direction for increasing values of t.

r(t)=(1+sint,3-cos2t),fort鈭�[0,2蟺]
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