2.1 Class Notes - Feb 13 lecture Practice Problem. Find the...

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Feb 13 lecture (x p ) = px p-1 (cf) = cf (f+g) = f +g (fg) = f g + f g (1/g) = - g / g 2 (f/g) = (f g - f g ) / g 2 (f(g)) = f (g) g (e x ) = e x (e g ) = e g g Practice Problem. Find the derivative of 2 x xe fg = f g + f g (e g ) = e g g 2 21 / 2 3/2 () ' 2 1 2 2 2 xx x x x x =⋅ ⎛⎞ +⋅ ⎜⎟ ⎝⎠ =+ Bases other than e ln3 ln 3 ( ) 3 Find '( ) Recall ( )' ' 3 3' ( l n 3 ) ( l n 3 ) 3 x gg x x fx f x ee g e = = == Newton’s law of cooling An object of temperature in a room of temperature (() ) (( 0 ) ) difference is reduced by 1/2 after time ln 2 / kt T R dT kT R dt Tt R T Re k =− −= CSI-Ithaca 0.0676 A dead body in a 68 room ( ) 68 30.6 e D Coroner’s rule of thumb: cools 2 degrees in first hour and 1 degree per hour after that
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Newton vs. the Coroner 70 75 80 85 90 95 100 0481 2 1 6 2 0 2 4 time in hours temperature About the exam 1 Formula sheet: The purpose of the formula sheet is so that you don’t have to memorize things.
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This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell University (Engineering School).

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2.1 Class Notes - Feb 13 lecture Practice Problem. Find the...

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