8. For the equation 4x³y = 3 +y³ — 6x² +5xy². the slope of the tangent line at the point (2,3) is =____.

【已刪除】4. 

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9. For the function f(x) = x3 - 3x2 - 24x 十 27 on the interval [-1,5], the absolute (global) maximum value is =____

10. The area between two curves y = 1 - x and y= ex from x = -1 to x = 4 is =____

【已刪除】1. Determine the improper integral dx is convergent or divergent.

2. Consider the function f(x,y) = 16xy -x4 -2y2, Find all relative extrema and identify any saddle point.

3. Find the volume under the surface f(x,y) =   and over the domain D which is the region hounded by curves y = x, x = 0 and y = 3.

【已刪除】1. A monopolist’s total cost (TC) and total revenue (TR) functions are assumed to respectively，where Q denotes the output quantity. The government is going to impose a tax of t dollars per unit quantity on the commodity produced by the firm. The government wants to maximize T=tQ, the total revenue it realizes from the tax. However, the government does not know what tax rate t will accomplish that end. Find the tax rate t that maximizes total tax revenue 丁 for the government and the equilibrium quantity Q for which the firm’s profit is maximized after taxation. (20 points)