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].

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:

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].

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