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110 年 - 110長庚大學_碩士班招生考試_工商管理學系︰微積分#101428 

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1. Find the valu of lim 614c1817354fc.jpg

2.2. 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 614c184758397.jpg . Indicate (if any) the asymptotes of the graph and  the coordinates of the relative extremes.


4. Find 614c186418a3e.jpg (the integral is fiom 0 to x) if it exists, otherwise indicate "does not exist."


5. Find 614c18845a343.jpg , if it exists or please indicate "it does not exist."


6. Evaluate the improperintegral 614c189fe36d2.jpg de if it converges, othervis inticate divergence.

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


8. Compute the double integral 614c18c607b97.jpgdA 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 614c19074694a.jpg, 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 614c19c878e8f.jpg valid for small 614c19d7d6a5c.jpg , show that it holds 614c19de88714.jpg.



(三)雖然企業是一種營利組織,透過販售商品和勞務以獲取利潤。但在現代社會中,企業也有其公民角色和責任。越來越多 的企業懂得「取之於社會,...

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110 年 - 110長庚大學_碩士班招生考試_工商管理學系︰微積分#101428-阿摩線上測驗

110 年 - 110長庚大學_碩士班招生考試_工商管理學系︰微積分#101428