3. Goods I and 2 are available at prices (in dollars) of p1 per unit of good 1 and p2 per unit of good 2. A utility function U(x1, x2) is a function representing the utility or beneit fo consuming xj, units of good j. The marginal utility of the jth good is 
, the rate of increase in utility per unit increase in the jth good. Prove the following law of economics: Given a budget of L dollars, utility is maximized at the consumption level (a,b) where the ratio of marginal utility is equal to the ratio of prices:
阿摩線上測驗
登入
dt.
have?
dA where R is the unit disk x2+ y2 ≤1.
dA where R is the interior of the ellipse
Use polar coordinates to show that f(x, y) is continuous at all (z, y) ifp ≤ 2, but discontin-
uous at (0,0) if p ≤ 2.
diverges or converges conditionally
or converges absolutely and give reasons for your answer. (6 points)
an converges,then
converges. (6 points)