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4. Find the values of a and b that makes the function differentiable at x = 0. Answer : _____________

其他申論題

(3) Find the gradient vector of the function f(x,y) := . Then find the equation of the tangent plane at (2,0).

1. Find the average value of g(x) = |x| - 1 on [-1,3]. Answer:__________

2. Find(x) dx. Answer :_______

3. Evaluatedxdy. Answer :___________

5. Find the tangent line to the curve x2 cos2y - sin y = 0 at (0,π). Answer :__________

6. Find the volume of the solid obtained by revolving the region bounded by the curves y = -x2 + 4x and y = x2 about the x-axis. Answer :____________

7. Evaluate . Answer :__________

8. Find the sum of the series Answer:_________

1. An open rectangular box is to be constructed from material that costs $3/ft2 for the bottom and $ 1/ft2 for its sides. Find the dimensions of the box of greatest volume that can be constructed for $36.

2. Use the limit definition to show that g'(0) exists butg', where

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