1205Test3F06key - Name ID AN S WE R KE Y Mat h 1 205 Class...

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Name ANSWER KEY Math 1205 Test 3 November 29, 2006 ID # Class Time or CRN READ THE DIRECTIONS. YOU MUST SHOW ALL WORK ON THIS TEST AND USE METHODS LEARNED IN CLASS OR FROM THE WORKSHEETS TO RECEIVE FULL CREDIT. CALCULATORS ARE PERMITTED. Pledge: I have neither given nor received help on this test. Signed 1. Use linearization to estimate 99.9 . f ( x ) = x ; a = 100 ; f (100) = 100 = 10 ! f ( x ) = 1 2 x ; ! f ( x ) = 1 2 100 = 1 20 L ( x ) = f (100) + ! f (100)( x " 100) L ( x ) = 10 + 0.05( x " 100) 99.9 # L (99.9) = 10 + 0.05(99.9 " 100) = 10 + 0.05( " 0.1) = 10 " .005 = 9.995 2 . The radius of a circular disk is given as 24 cm with a maximum error in its measurement of 0.2cm. a. Use differentials to estimate the maximum error in the calculated area of the disk. r = 24 cm A = ! r 2 " r = 0.2 cm " A # dA = 2 ! rdr dA r = 24 cm " r = 0.2 cm = 2 ! (24)(0.2) = 9.6 ! cm 2 # 30.15928947 cm 2 b. Use the part a answer to estimate the percentage error. % Error = ! A A (100) " dA A (100) % Error " 9.6 # # (24) 2 (100) = 9.6 # 576 # (100) = 0.01 6 6(100)= 1. 6 6% 3. Find the third degree Taylor Polynomial centered at x = ! 2 for f ( x ) = sin( x ) .
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f ( x ) = sin( x ) f ( ! 2 ) = sin( ! 2 ) = 1 " f ( x ) = cos( x ) " f ( ! 2 ) = cos( ! 2 ) = 0 "" f ( x ) = # sin( x ) "" f ( !
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