3.The demand function for a product is modeled by 

p=1/(0.000001x³+0.01x+1) 

where p is measured in dollars and x is measured in thousands of units. Find the rate of change of the demand x with respect to the price p when x=100.

1.The demand and supply equations for an e‐book reader are given by p = 195 -3.8x q = 150 +3.2xwhere p is the price in dollars and x represents the number of units in millions. Find the equilibriumpoint for this market.

2.Find an equation of the tangent line to the graph of y= at  x=1.

4.Show that the graph of the normal probability density function f(x)= has points of inflection at x=±1.

5.The marginal cost of producing x units of a product is modeled by.  It costs $50 to produce one unit. Find the total cost of producing 200 units.

6.Find the area of the region bounded by the graphs of f(x)=3x3-x2-10x and g(x)=-x2+2x.

7.A manufacturer’s production is modeled by the cobb‐Douglas function f(x,y)= Where x represents the units of labor ( at $ 150 per unit ) and y represents the units of capital ( at $ 250 per unit ). The total cost for labor and capital cannot exceed $ 50,000. Will the manufacturer’s maximum production level exceed 16,000 units? ( Hint: Use the method of Lagrange Multipliers and the funciton . F(x,y,λ)=f(x,y)-λ(150x+250y-50,000).)

8.A. Find the limit.

B. Evaluate by interpreting it in terms of areas.

C. Use the Fundamental Theorem of Calculus to find the derivative of the function.

D. Use logarithmic differentiation to find the derivative of the function.

113年 - 113 國立嘉義大學_轉學生招生考試試題_(全校)：微積分#122986

112年 - 112 國立臺灣大學_碩士班招生考試題：微積分(D)#130254

112年 - 112 國立陽明交通大學_碩士班入學招生試題_統計學研究所﹕微積分與線性代數#130252

112年 - 112 國立嘉義大學_轉學生招生考試試題：微積分#123297

112年 - 臺灣綜合大學系統112 學年度學士班轉學生聯合招生考試試題 微積分A#120563

112年 - 112 臺灣聯合大學系統(清華、陽交、中央 聯招)學士班轉學生考試_A3、A4、A6理工組：微積分#117689

112年 - 112 臺灣聯合大學系統(清華、陽交、中央三校聯招)學士班轉學生考試_A2商管組：微積分#117687

112年 - 112 國立高雄師範大學轉學生招生考試試題_電子工程學系二年級：微積分#116290

112年 - 112 國立高雄師範大學_轉學生招生考試試題_電機工程學系二年級：微積分#116289

111年 - 111 國立臺北大學_轉學生招生考試試題_經濟學系二年級：微積分#117728