This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: cos Î¸ Â· Î¸ = 1 12 x . Hence, Î¸ = x 12 cos Î¸ Â± Â± Â± x =3 ,Î¸ = 2 Ï€ 3 = 1 2 radian/sec . 2. Set f ( x ) = 3 âˆš x . The linearization of f at x = 27 is then L ( x ) = f (27) + f (27)( x27) = 3 + 1 27 Â· ( x27) . Hence, f (26) â‰ˆ L (26) = 3 + 1 27 Â· (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 âˆˆ ( a,b ) such that f ( c ) = f ( b )f ( a ) ba . So sin c = cos bcos a ba . It implies Â± Â± Â± cos bcos a ba Â± Â± Â± =  sin c  â‰¤ 1 . 3...
View
Full Document
 Spring '07
 Tuffaha
 Math, Differential Equations, Linear Algebra, Algebra, Trigonometry, Equations, Derivative, Cos, MVT

Click to edit the document details