Represent the following curve by a vector-valued function.
A)
B)
C)
D)
E)

Name: Represent the following curve by a vector-valued function. A) B) C) D) E)
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Question

Represent the following curve by a vector-valued function. ​  ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

The curve has an oscillatory behavior suggesting a sinusoidal function. Moreover, the y-component of the vector function varies periodically between -1 and +1, with its maximum near 0. Thus, a possible vector function would be:

r(t) = cos(t) i + sin(t) j + k

which matches the form of option C.

Represent the Following Curve by a Vector-Valued Function