105年 - 105 國立海洋大學轉學生招生考試試題_共同科目：微積分#116641

科目：研究所、轉學考(插大)-微積分 | 年份：105年 | 選擇題數：0 | 申論題數：16

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所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (16)

(a)

(b)

(a)

(b) y=(Inx)^x

3.(6 分)Consider the function f(x)= 3x + cosx, Find the value of (f^-1)'(1).

4. (6 分) Find the equation of the tangent line to the curve x³+ y³ = 6xy at the point (3,3).

5. (6 分) Use a linear approximation (or differentials) to estimate the number.

6. (8 分) Car A is traveling west at 90 km/h and car B is traveling north at 100 km/h. Both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 6 km and car B is 8 km from the intersection?

(a) ∫xsec² xdx

(b)

(c)

(d)

(a) Given f(x,y)=, find f_x(x,y).(4分)

(b) Given x ln y+y²z+z² =5, find

(c) Find the maximum value of the directional derivative at the given point:

f(x,y)= ycos(x-y), point:

9. Find the interval of convergence of ∫f(x)dx, where (10分)