105年 - 105 東吳大學_暑假轉學生招生考試_經濟學系二年級：微積分#115944

(a)

(b)

(a)

(b)g(x)=x²(3x²+2)²

(c)h(x)=

3. Find the absolute extrema of the function f(x)= on [2,5].

(a)

(b)

(c)

5. It is found that the Lorenz curve for the distribution of income of college teachers is described by the function

Compute the coefficient of inequality for the Lorenz curve (the Gini Index of Lorenz curve).

6. Find the extrema of the function f(x,y,z)=x+y+z subject to the constrain z=2x²+4y².

7. Evaluate the double integral

for the function f(x,y)= and the region bounded by y=x,y=2x and y=.

8. Use the fifth Taylor polynomial at x=0 to approximate the area the graph of f(x)-ln(1+x) from x=0 to x=1.

9. Determine the relative extrema of the function
f(x)=
using the second derivative test.

105年 - 105 東吳大學_暑假轉學生招生考試_經濟學系二年級：微積分#115944

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