T1-S47 - Name: Northwestern University Id #: Math 230...

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Northwestern University Name: Id #: Math 230 Section 47 Test #1 Fall Quarter 2007 Tuesday, October 23, 2007 Name: Instructions: Show all your work on these sheets. Feel free to use the opposite side. Make sure that your final answer is clearly indicated. This test has seven problems. No calculators, books, notes, etc. are allowed. Good luck! Prob. Possible Score points 1 25 2 20 3 20 4 25 5 10 TOTAL 100
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Math 230 Section 47 Test #1 Fall Quarter 2007 Page 2 of 11 BLANK PAGE
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Math 230 Section 47 Test #1 Fall Quarter 2007 Page 3 of 11 Question 1. Answer the following questions with respect to the given curve below: r ( t ) = (sin 2 t ) i + (cos 2 t ) j , 0 t π 2 (13 points) Find the curve’s unit tangent vector at t = π 4 . Solution: r ± ( t ) = (2 sin t cos t ) i + ( - 2 sin t cos t ) j T ( t ) = r ± ( t ) | r ± ( t ) | = (2 sin t cos t ) i + ( - 2 sin t cos t ) j p (2 sin t cos t ) 2 + ( - 2 sin t cos t ) 2 = (2 sin t cos t ) i + ( - 2 sin t cos t ) j p (8 sin 2 t cos 2 t ) = (2 sin t cos
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T1-S47 - Name: Northwestern University Id #: Math 230...

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