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Unformatted text preview: cos = 1 12 x . Hence, = x 12 cos x =3 , = 2 3 = 1 2 radian/sec . 2. Set f ( x ) = 3 x . The linearization of f at x = 27 is then L ( x ) = f (27) + f (27)( x27) = 3 + 1 27 ( x27) . Hence, f (26) L (26) = 3 + 1 27 (2627) = 80 27 . It is over estimate, since the tangent line will be above the curve of f . 3. It is obvious if a = b . In the rest, we will prove when b 6 = a . Let f ( x ) = cos x . Then (a) f is continuous. (b) f is continuous. By MVT, there exits c ( a,b ) such that f ( c ) = f ( b )f ( a ) ba . So sin c = cos bcos a ba . It implies cos bcos a ba =  sin c  1 . 3...
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 Spring '07
 Tuffaha
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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