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Unformatted text preview: M408C Homework: 10/2 10/25
10/2 Find dy/dx using normal implicit differentiation, and then using the partial derivative shortcut: (1) tan(x2 y) = x3 sin(xy 3 ) (2) x3 + y 4 = x4 y 3 + 9 For (2), find the equation of the tangent line at the point (1, 2). 10/4 Differentiate: (1) y = ln(csc x) (2) y = cot(ln x) (3) y = sin3 (ln2 (1/x)) 10/11 No homework assigned. 10/16 Differentiate: (1) (2) (3) (5) y y y y = arctan(x3 ) = arcsin(1/x) = ln(arctan(x)) = e1/ arctan( x) Using a right triangle, calculate the following: (6) cos(arcsec(x)) (7) sin(arccot(x)) 10/18 From the textbook: page 262, #4, 7, 8, 11, 13. 10/23 From the textbook: page 263 #30, 33, 36, 41, 66. Also, in #72 from the same page: By symmetry we expect there to be a critical point at x = 5. Is this a local maximum or a local minimum? [Use the 2nd derivative test.] 10/25 Finish page 264, #38, which was started in lecture (assuming that the volume is 1). Show that the "ideal" ratio r/h is 2/2. ...
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This homework help was uploaded on 04/09/2008 for the course M 408c taught by Professor Mcadam during the Fall '06 term at University of Texas at Austin.
 Fall '06
 McAdam
 Derivative, Implicit Differentiation

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