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

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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
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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## This note was uploaded on 11/23/2008 for the course CHEM 210-1 taught by Professor Trzupek during the Fall '08 term at Northwestern.

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T1-S47 - Name Northwestern University Id Math 230 Section...

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