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Chapter 11: Q. 10 (page 859)

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�).)

Short Answer

Expert verified

The graph of r may be contained in a circle centered at the origin.

Step by step solution

01

Step 1. Given Information.

The given vector-valued function isr(t)=xt,yt,t鈭�[a,鈭�).

02

Step 2. Explanation.

To explain the graph of r may or may not be contained in a circle centered at the origin, let r1t=1t,1twithdomain[1,鈭�).

Now, the graph of r1(t)is

03

Step 3. Explanation.

Now, let r2t=t,twithdomain[1,鈭�).

The graph of r2(t)is

From both graphs, we can depictr that may be contained in a circle centered at the origin.

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