104年 - 104 國立臺北大學學士班暨進修學士班轉學生招生考試試題_資訊工程學士、通訊工程學系：微積分#116800

(a) with y as the variable of the integration, ie write. (5%)

(b) with x as the variable of the integration, ie write (5%)

2.(20%) The Cobb-Douglas Model for the production function is P=bL^aK^1-a , where b and a are positive constants and a ＜1. We want to maximize the production Pwith the constraint that mL+nK =q, where m, n and q are positive constants. Show that the maximum production occurs when

(a)

(b)

(c)

(d)

5. (20%)Please sketch the curve y = . (You must describe the domain, intercepts, symmetry, asymptotes, interval of increasing or decreasing, local maximum and minimum values, and concavity and points of inflection.)

 6.(5%)Prove using the ε,δ definition of a limit.

7. (5%)Find if ycosx = 1 + sin(xy).