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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)( x-27) = 3 + 1 27 ( x-27) . Hence, f (26) L (26) = 3 + 1 27 (26-27) = 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 ) b-a . So sin c = cos b-cos a b-a . It implies cos b-cos a b-a = | sin c | 1 . 3...
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