Instructor: K. W. Nicholson
Test for convergence and absolute convergence.
1.
2.
3. Find the interval of convergence (include checking endpoints).
4. Find the first 4 terms of the Taylors series expansion of f(x) = sin x, expanded about
a = ¹/3.
5. Use the Maclurin's series expansion for f(x) = -1/ (1+x) to obtain a Maclurin's series expansion for
f(x) = 1 / (1+x)2
Tell whether the following series converges or diverges. If it converges, state the number to which it converges.
6. 
Test for convergence using any test you choose. You must give which test you used and reasons for its conclusion.
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12. Find dz/dt : z = x3 - y, if x = t e t, y = sin t.
13. Find the equation of the tangent plane with normal line to z = x2 - 2y2 at (2,1,2).
14. Find the directional derivative of w = x y z2 in the direction of the v = i - 2j + 2k.
Find all the critical points and test for relative maximum and minimum for each of the following.
15. z = 2y3 + x2 - y2 - 4x - 4y + 1
10 Points Bonus!
A vertical line is moving to the right at 2 cm/min., and a horizontal line is moving upward at 3 cm/min. Find the rate of change of the area of the rectangle formed by the coordinate axes and these two lines at the moment when the lines are x = 5 and y = 4.