96年 - 96 東吳大學轉學生(含進修學士班)招生考試試題_經濟學系：微積分#116774

(a)Is the function f(x) continuous at x=1?

(b)Is the function f(x) differentiable at x=1? (6%)

(a)

(b) (6%)

(3) Solve the differential equation (6%)

(4) Find for the function x=4t+6 y=t²+t-2 (6%)

(a)

(b) (10%)

(c)∫x(x+1)dx

(d)

(6) Find the maximum of the function f(x,y,z)=xyz subject to the constrain 6x+4y+3z=24. (6%)

(7) The marginal cost for producing x units of a product is modeled by =32-0.04x. It costs $ 50 to produce one unit. Find the total cost of producing 10 units? (6%)

(8) Find the area of the region bounded by the graph of the equation y² =4x²-x⁴ (6%)

(9) Find the Taylor' s series for f(x)=sinx in power of (6%)

(10) Find the point of the graph of the equation y= x² that is nearest the point (3,0) (6%)

(11) A business sells 2000 units of product per month at a price of $10 each. It can sell 250 more items per month for each $0.25 reduction in price. What price per unit wil l maximize the monthly revenue? (6%)

(12) Sketch the graph f(x)=xe^x (6%)

(13) Find the equation of the tangent l ine to the curve x² -xy+ y²= 7 at the point (-1,2) (6%)

(a)

(b) (6%)

(15) Find the volume of the solid generated by revolving the region between the x-axis and curve 1≤x≤4 about the x-axis(6%)

(16) Find the volume of the solid region bounded in the first octant by the plane z=2-x-2y (6%)

96年 - 96 東吳大學轉學生(含進修學士班)招生考試試題_經濟學系：微積分#116774

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