Real Analysis Conception Question 1. Lemma: if P is a subset of Q, then L(f,p)<=L(f,Q) and...

Real Analysis Conception Question

1. Lemma: if P is a subset of Q, then L(f,p)<=L(f,Q) and U(f,P)>=U(f,Q)

why??? for P is a subset of Q, however, why the upper sum of U(f,P) is even bigger than or equal to U(f,Q) it doesn't make any sense. Please

draw the geometric description to help with clear hand written

2. Let's assume the partition={x0,x1...xn} of the interval [a,b]

what is the diference between m=inf{f(x):x is a element of [a,b]} and mk=inf{f(x):x is a element of [xk-1,xk]}

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.)...

Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.) Why does this equivalency allow us to use the proof by contradiction technique?

A firm produces output according to the following function: q = f (L, K) = L^1/2...

A firm produces output according to the following function: q = f (L, K) = L^1/2 K^1/4 . The cost of labor is $8 per hour and the rental cost of capital is $2 per hour. a. Determine the returns to scale for this function. b. Suppose the firm wishes to produce at cost $96. How much capital and how much labor does the firm employ? c. Derive the short-run cost function with optimal amount of K from part b....

1. Show that the argument (a) p → q q → p therefore p...

1. Show that the argument (a) p → q q → p therefore p V q is invalid using the truth table. ( 6 marks ) (b) p → q P therefore p is invalid using the truth table. ( 6 marks ) (c) p → q q → r therefore p → r is invalid using the truth table. ( 8 marks )

Conception of the Integral and convergence of the function 1. We know that if fn—->f is...

Conception of the Integral and convergence of the function 1. We know that if fn—->f is (point-wise or uniformly)and every fn in the interval is Riemann integral, then will f be Riemann integrable on [a,b]? please answer this question separately in pointwise and uniformly.

Consider the production function from question 1: q = L^1/5 K^4/5. Marginal cost is $5, P=(8−...

Consider the production function from question 1: q = L^1/5 K^4/5. Marginal cost is $5, P=(8− 1 2q), and FC = $1. (a) What is II*? That is, what is the maximum profit? (b) Should this company shut-down based on profit function, q*, maximum profit? (c) Suppose that the profit amount found in (a) is the long-run equilibrium profit. Is this company in a perfectly competitive market?

Let T∈ L(V), and let p ∈ P(F) be a polynomial. Show that if p(λ) is...

Let T∈ L(V), and let p ∈ P(F) be a polynomial. Show that if p(λ) is an eigenvalue of p(T), then λ is an eigenvalue of T. Under the additional assumption that V is a complex vector space, and conclude that {μ | λ an eigenvalue of p(T)} = {p(λ) | λan eigenvalue of T}.

Real numbers p and q are randomly chosen from the interval 0 to 1, inclusive. If...

Real numbers p and q are randomly chosen from the interval 0 to 1, inclusive. If r is given by r = 2(p + q), and p, q, r are rounded to the nearest integers to give P, Q and R, respectively, determine the probability that R = 2(P + Q). (As an example, if p=0.5 and q=0.381, then r=1.762, and so P =1, Q=0, and R=2)

Suppose that output Q is produced with the production function Q = f(K;L), where K is...

Suppose that output Q is produced with the production function Q = f(K;L), where K is the number of machines used, and L the number of workers used. Assuming that the price of output p and the wage w and rental rate of capital r are all constant, what would the prot maximizing rules be for the hiring of L and K? (b) What is theMRTSK;L for the following production function: Q = 10K4L2? Is this technology CRS, IRS or...

Suppose that output Q is produced with the production function Q = f(K,L), where K is...

Suppose that output Q is produced with the production function Q = f(K,L), where K is the number of machines used, and L the number of workers used. Assuming that the price of output p and the wage w and rental rate of capital r are all constant, what would the proﬁt maximizing rules be for the hiring of L and K? (b) What is the MRTSK,L for the following production function: Q = 10K4L2? Is this technology CRS, IRS...

Consider an industry with n identical firms competing a l´a Cournot. Demand is P(Q) = 1...

Consider an industry with n identical firms competing a l´a Cournot. Demand is P(Q) = 1 − Q, and each firm’s total cost function is T C(qi) = cqi . (a) Find the limit of the total equilibrium output Q∗ (n) as n goes to infinity. (b) Suppose that n > 3 and 3 firms decide to merge. The new firm has the same total cost function as its predecessors. What is the condition on n that ensures that the...

Subjects