Three-Sector Economy In Exercises 1–12, suppose that a simplified economy consisting of the three sectors Manufacturing, Energy, and Services has the input–output matrix
Repeat Exercise 11 for the consumer demand matrix
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- Is the function f(x) shown in the graph below continuous at x = −5? f(x) 7 6 5 4 2 1 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 Select the correct answer below: The function f(x) is continuous. ○ The right limit exists. Therefore, the function is continuous. The left limit exists. Therefore, the function is continuous. The function f(x) is discontinuous. ○ We cannot tell if the function is continuous or discontinuous.arrow_forward1.3. The dots of Output 2 lie in pairs. Why? What property of esin(x) gives rise to this behavior?arrow_forward1.6. By manipulating Taylor series, determine the constant C for an error expansion of (1.3) of the form wj−u' (xj) ~ Ch¼u (5) (x;), where u (5) denotes the fifth derivative. Based on this value of C and on the formula for u(5) (x) with u(x) = esin(x), determine the leading term in the expansion for w; - u'(x;) for u(x) = esin(x). (You will have to find maxε[-T,T] |u(5) (x)| numerically.) Modify Program 1 so that it plots the dashed line corresponding to this leading term rather than just N-4. This adjusted dashed line should fit the data almost perfectly. Plot the difference between the two on a log-log scale and verify that it shrinks at the rate O(h6).arrow_forward
- 4. Evaluate the following integrals. Show your work. a) -x b) f₁²x²/2 + x² dx c) fe³xdx d) [2 cos(5x) dx e) √ 35x6 3+5x7 dx 3 g) reve √ dt h) fx (x-5) 10 dx dt 1+12arrow_forwardDefine sinc(x) = sin(x)/x, except with the singularity removed. Differentiate sinc(x) once and twice.arrow_forward1.4. Run Program 1 to N = 216 instead of 212. What happens to the plot of error vs. N? Why? Use the MATLAB commands tic and toc to generate a plot of approximately how the computation time depends on N. Is the dependence linear, quadratic, or cubic?arrow_forward
- Show that the function f(x) = sin(x)/x has a removable singularity. What are the left and right handed limits?arrow_forward18.9. Let denote the boundary of the rectangle whose vertices are -2-2i, 2-21, 2+i and -2+i in the positive direction. Evaluate each of the following integrals: (a). 之一 dz, (b). dz, (b). COS 2 coz dz, dz (z+1) (d). z 2 +2 dz, (e). (c). (2z+1)zdz, z+ 1 (f). £, · [e² sin = + (2² + 3)²] dz. (2+3)2arrow_forwardWe consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…arrow_forward
- eric pez Xte in z= Therefore, we have (x, y, z)=(3.0000, 83.6.1 Exercise Gauss-Seidel iteration with Start with (x, y, z) = (0, 0, 0). Use the convergent Jacobi i Tol=10 to solve the following systems: 1. 5x-y+z = 10 2x-8y-z=11 -x+y+4z=3 iteration (x Assi 2 Assi 3. 4. x-5y-z=-8 4x-y- z=13 2x - y-6z=-2 4x y + z = 7 4x-8y + z = -21 -2x+ y +5z = 15 4x + y - z=13 2x - y-6z=-2 x-5y- z=-8 realme Shot on realme C30 2025.01.31 22:35 farrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forward
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