110年 - 110 國立中央大學_碩士班招生考試_財務金融學系/乙組(一般生):微積分#103831

Instruction: This is a closed book exam. There are 10 problems and each is worth 10 points. Write everything CLEARLY, any ill-explanation or bad handwriting on your answer sheet should cause no credits. It is YOUR responsibility to turn in a clean, well-organized answer sheet.
Problem (1) Find exp(az) cos (bx)dn.

Problem (3) Find the relative extrema of the function
 f(x, y) = x³ - 12xy + 8y³, (x,y)

Problem (4) Find the interval of convergence of the following series:

Problem (5) Find the particular solution of

Problem (6) Let

 If is clear that O is a root of f(x) = 0. Use Newton's method with initial xo = 1 to obtain a sequence of "approximations". Does the above "approximations" approach 0? If not, give the reason. 

Problem (8) Show that
You can prove this by first showing that

Problem (10) Find
 if it exists.