1. Find the valu of lim

2. Find the value of the constant c such that g(x) is continuous on all real numbers, where 

3. Sketch the graph of the function . Indicate (if any) the asymptotes of the graph and  the coordinates of the relative extremes.

4. Find (the integral is fiom 0 to x) if it exists, otherwise indicate "does not exist."

5. Find , if it exists or please indicate "it does not exist."

6. Evaluate the improperintegral de if it converges, othervis inticate divergence.

7. Find the Taylor series at x =1 for In x, and find its interval of convergence.

8. Compute the double integral dA where R is the rectangular region 0≤x≤2, and O≤y≤1.Also, dA indicates either dydx or dxdy may be used.

9. Suppose that a company's output is given by the Cobb-Douglas production function , where L and K are the numbers of units of labor and capital that are used. To stay within its budget of $2520, these amounts must satisfy 35L +140K = 2520 . Find the amounts of labor and capital that maximize production subject to the budget constraint.

10. The 72 rule says that money invested at 6% per year doubles in approximately 12 years. Also, money invested at 8 % per ycar doubles in approximately 9 years. Suppose that the number of years n is required for an investment at interest rate r to double in valuc, and i is the interest rate percentage (that is, i =100r). Using In2 = 0.693 and the approximation valid for small , show that it holds .

1.關於衛生福利部修訂醫療機構設立或擴充辦法限制慢性一般病床的設立許可，請寫出此種作法對於長期照護產業的發展有何影響?

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