Find the Open Interval on Which the Curve Given by the Vector-Valued

question 51

Multiple Choice

Find the open interval on which the curve given by the vector-valued function $r ( \theta ) = ( 6 \theta + 6 \sin \theta ) \mathbf { i } + ( 8 - 6 \cos \theta ) \mathbf { j }$ is smooth.

• A) \(( ( 4 n - 8 ) \pi , ( 3 n + 2 ) \pi )\)
• B) \(( ( 2 n - 8 ) \pi , ( 2 n + 8 ) \pi )\)
• C) \(( ( 3 n - 1 ) \pi , ( 3 n + 1 ) \pi )\)
• D) \(( ( 2 n - 1 ) \pi , ( 2 n + 1 ) \pi )\)
• E) \(( ( 3 n - 8 ) \pi , ( 4 n + 2 ) \pi )\)

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