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Math 201 (section 3)
November 1, 2004

Homework 10 (due Monday, November 8)

Note: Homework 9 is due Wednesday, November 3.

Read about quadratic approximations, p. 1000, and the second derivative test, p. 990.
Read the part of Section 14.3 about arc length (ending with the heading "curvature" on page 900) Review pages 699-701 (in section 11.2) if it helps; and review as much about integrals as it takes for section 14.3 to make sense. Try to get the key idea of "parameterization by arc length."
Read ahead Sections 16.1 and 16.2, on double integrals over rectangular regions. Review as much about definite integrals as it takes for this to make sense.


Quiz Monday, Nov. 8 --- about definite integrals, details TBD.


Problems to turn in (Nov. 8)

About second derivative test: Section 15.7 (p. 997) 1ab and 2a. You're supposed to say, if you can, whether the given critical point is a local maximum, local minimum, or saddle point.

About quadratic approximation: Do...

Problem K. Let f(x,y) = sin(xy), and let (a,b)=(0,0).
a. Write formulas for the functions f_x, f_y, f_xx, f_xy, f_yy. (The underscore indicates a subscript.)
b. Calculate the numbers: f(0,0), f_x(0,0), f_y(0,0), f_xx(0,0), f_xy(0,0), f_yy(0,0).
c. Now let (x,y) = (0.40, 0.80). What are:
   f(x,y)?
   L(x,y) (the linear approximation, at (x,y)) ?
   Q(x,y) (the quadratic approximation, at (x,y)) ?

Problem L. Let f(x,y) = 1 + 2x + x^2 + xy.    (x^2 means x squared.)
   Write a formula for the quadratic approximation Q(x,y), using (a,b)=(0,0).

About arc length: Section 14.3 (p. 904), 3, 5, 7. For problem 7, just set up the integral explicitly---you don't need to use Simpson's rule or evaluate the integral.

(end)


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