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題組內容

一、

4. (14%) Use Simpson's rule with n=10 to approximately compute

其他申論題

(3) How does the lambda phage establish its lysogenic cycle? (5 points)

1. (12%) Compute xdx.

2. (12%) Find the area enclosed by the equation .

3. (12%) Compute dx.

1. (8%) Prove that limx→2(3x-1)= 5.

2. (8%) Show that the function is continuous on the interval [-2,2].

3. (8%) Show that the function f(x) = x2 -x + 1 is differentiable for

4. (8%) Suppose that f(0) = 0 and f'(x) ≥6 for . How small can f(100) possibly be?(Hint: the Mean Value Theorem)

5. (6%) Find y' if x4 +y4 =8xy2.

6. (6%) Find y' if y = cos(xcos x).

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