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Unformatted text preview: ( x,y ) (0 , 0) xy x 2 + y 2 as ( x,y ) approaches the origin along (a) the x-axis (b) the line y = 2 x (c) the spiral r = , > (d) along the path ~ r ( t ) = 1 t ~ i + sin t t ~ j , t > 0. Does lim ( x,y ) (0 , 0) xy x 2 + y 2 exist? Explain. 3. A petrochemical company is designing a cylindrical tank with hemispher-ical ends to be used in transporting its product. (a) Find the volume of the tank as a function of the radius r and height h of the cylindrical portion of the tank. (b) If h held xed, nd the rate of change of the volume with respect to r . 4. Calculate the four second order partial derivatives of f ( x,y ) = e xy 2 . 1...
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This note was uploaded on 10/14/2009 for the course M 408d taught by Professor Sadler during the Spring '07 term at University of Texas at Austin.
- Spring '07