PLEASE ASSIST WITH BOTH OF THEM Question 2 2.1 Derive the following O(h) three-point formula (including...
Theorem 2.1 Consider an IVP of the form y' + g (x)ya h(x), y(%)-yo. Assume that g(x) and h(x) are both continuous on some interval a < x < b and that a < xo < b. Then there exists a unique solution y(x) to the initial value problem that is defined on a <x<b Theorem 2.2 Consider an IVP of the form y' = f (x.y), y(xo) = yo. Assume that ftxy) andfx, y) are both continuous on a...
Exercise 4.6-2: Find the optimal value for h that wll minimize the error for the formula f' (xo) = f(x0+h) _ f(xo) _ h f"(e) in the presence of roundoff error, using the approach of Section 4.6 a) Consider estimating f(1) where f(x)using the above formula. What is the optimal value for h for estimating f'(1), assuming that the roundoff error is bounded by E-10-16 (which is the machine epsilon 2-53 in the 64-bit floating point representation). b) Use Julia...
CALCULUS Consider the function f : R2 → R, defined by ï. Exam 2018 (a) Find the first-order Taylor approximation at the point Xo-(1, -2) and use it to find an approximate value for f(1.1, -2.1 (b) Calculate the Hessian ã (x-xo)' (H/(%)) (x-xo) at xo (1,-2) (c) Find the second-order Taylor approximation at Xo (1,-2) and use it to find an approximate value for f(1.1, -2.1) Use the calculator to compute the exact value of the function f(1.1,-2.1) 2....
Please Solve in C programming. Please Use “ f(x) = e^(-x^2) “ for thus question. Thank You rite computer code in any programming language or mathematical software to estimate he following derivatives. Then calculate the absolute and relative errors for each: I, f"(1.5) for f(z) in Question 3 above using the three-point formula. Use h 0.5 rite computer code in any programming language or mathematical software to estimate he following derivatives. Then calculate the absolute and relative errors for each:...
Quantum Mechanics Thank you! 2 Casimir effect We will derive the Casimir effect in three dimensions, making use of the Euler- Maclaurin formula Ž 0,F(n) – [F(n)dn = 67\2F'O) + 30 x , F"(0) -... (1) JO n=0 where On = 1 for n > 0, 0 = 1/2, and on = 0 for n < 0. (You don't need to prove this formula.) Let us consider a square box with conducting walls of length L. Let El be the...
please answer them in detail. The concentration C(x, t) of a pollutant in a semi-infinite pipe diffuses according to the PDE over 0<<o for > 0, where the diffusivity D is a given positive constant. An experiment is performed in which the initial concentration is zero everywhere, so that C(x, 0)0 for all r 20. Once t > 0 a fixed concentration of C(0, t) Co is imposed at x-0, where Co is a constant, and it is also assumed...
only answer (h)please 2 Short Answer Solve the following problems and answer concisely. 2.1 Guns and Crime (15 points) The following regression table shows the estimation results studying the relationship between guns and crime rates in the United States (5) Violet (1) Los violent -0.000 0.05) (2) Log violent -0.2156 100 (6) Lagrobbery) -0.1276 (4) log violet) Logi t) -0.1436 0.0165) 10.12) 0.1259 0.00211 0056) 0.001) Concealed Carry law -02179 incarceration rate 0.0519 log incarceration rate 2.95 (17.68) percent male...
only answer (f)please 2 Short Answer Solve the following problems and answer concisely. 2.1 Guns and Crime (15 points) The following regression table shows the estimation results studying the relationship between guns and crime rates in the United States (5) Violet (1) Los violent -0.000 0.05) (2) Log violent -0.2156 100 (6) Lagrobbery) -0.1276 (4) log violet) Logi t) -0.1436 0.0165) 10.12) 0.1259 0.00211 0056) 0.001) Concealed Carry law -02179 incarceration rate 0.0519 log incarceration rate 2.95 (17.68) percent male...
photos for each question are all in a row (1 point) In the following questions, use the normal distribution to find a confidence interval for a difference in proportions pu - P2 given the relevant sample results. Give the best point estimate for p. - P2, the margin of error, and the confidence interval. Assume the results come from random samples. Give your answers to 4 decimal places. 300. Use 1. A 80% interval for pı - P2 given that...
only answer (b)please Short Answer 2. Solve the following problems and answer concisely 2.1 Guns and Crime (15 points) The following regression table shows the estimation results studying the relationship between guns and crime rates in the United States (6) Log(robbery) (4) Log(violent) Log(violent) Log(violent) Log(violent) -0.1436 (0.1236) (1) (2) (3) (5) Violent concealed carry-law -0.4430 (0.0475) -0.2479 (00145) -122.88 (80.03) -0.2456 (0.0368) -0.1276 (0.0902) incarceration rate 0.1259 (0.0056) 0.0211 (0.0017) 336.31 (12.72) 0.0519 (0.0001) 2.984 log incarceration rate (17.68)...