3.=__(D)__

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:

b. Show that if an converges,then converges. (6 points)

1.The upper sum = __(A)__. and the lower sum = __(B)__ if f(x) := |x|,x ∈ [-2,1] and P is the partition of [-2,1].

2.=__(C)__

4.=__(E)__ for x＞ 0.

5.The radius of convergence of the power series =__(F)__

6.The Maclaurin serics for sin(x + 1) =__(G)__

7.=__(H)__

(a) If f(x) :=x3 - 2x + 2, x ∈ , then f has a zero between -2 and 0.

(b) Consider two series. Suppose ≥ 0 and . If converges, then converges.