# s10fes - 92-131 1 3x csc x cot x 2 3 Final Exam(Solutions...

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Unformatted text preview: 92-131 1. - 3x csc x cot x 2 3 Final Exam (Solutions) Spring 2010 ( ) ( ) 3 -1 2 2 xe tan (x ) 2. 1+ x4 3. cos 2 ( x) - sin 2 ( x) = cos(2 x) ( ) 4. - t 4 + 3t 2 + 2t (t 3 +1 ) 2 5. - 25 ln x x6 6. 20( x + 1) x 2 + 2 x + 4 ( ) 9 3( x + h) 2 + 4( x + h) - 3x 2 + 4 x f ( x + h) - f ( x ) = lim 7. f ( x) = lim h0 h0 h h = lim [ [ 3x 2 + 6 xh + 3h 2 + 4 x + 4h - 3 x 2 - 4 x 6 xh + 3h 2 + 4h = lim h0 h0 h h = lim[6 x + 3h + 4] = 6 x + 4 h0 Power rule is d k d d d x = k x k -1 . (3 x 2 + 4 x) = (3 x 2 ) + (4 x) = 6 x + 4 dx dx dx dx 8. (sin t ) [ln sin t + t cot t ] t 9. (a) - 42 m / s (b) 2 sec (c) s(t ) = 2t 2 - t4 2 (b) max f (2) = 4 e2 10. (a) incr (0, 2) decr (-, 0) and (2, ) (c) conc up - , 2 - 2 min f ( 0) = 0 ( ) (2 + 2 , conc down 2 - 2 , 2 + 2 ) ( ) (d) vertical asymptote: none (domain is all real numbers) horizontal asymptote: y = 0 (the limit of the function as x ) 11. height: 12. 2 3 ft 3 2 radius: 6 ft 3 (a) x n +1 = x n - xn - 2 xn + 2 = 2 xn 2 xn 2 (b) x1 = 3 2 x2 = 17 1.416667 12 ...
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## This note was uploaded on 02/13/2012 for the course MATH 92.131 taught by Professor Staff during the Fall '09 term at UMass Lowell.

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