9. With Y as in #8, and using the de Moivre Laplace approximation, approximate P(12 〈 YÇ i8). no...
Q1) Solve the following DE: (Using Laplace transform is recommended) y" + 5y' – 6y = f(t), y(0) = 0, y'(0) = 0, where 0 <t< 2 f(t) = {-4 t>2 1
Consider the graph 12 10 6, 9) y-f(x 8 (2, 7) (4, 5) (0, 3) (8, 0) 10 (a) Using the indicated subintervals, approximate the shaded area by using lower sums s (rectangles that lie below the graph of f) (b) Using the indicated subintervals, approximate the shaded area by using upper sums S (rectangles that extend above the graph of f) +-14 points SullivanCalc1 5.1.019 Approximate the area A under the graph of function f from a to b...
Topic: Normal approximation to binomial distribution Calculate the following probabilities using a normal approximation. P(9 ≤ X ≤ 12) where X ∼ B(21, 0.5) Please show work as I will studying it step by step, thanks.
(1) (a) Argue using the Central Limit Theorem that one may approximate X ~ by a normal law when n is large. (b) Under the CLT approximation, find a so that P(X > a)- 10 (1) (a) Argue using the Central Limit Theorem that one may approximate X ~ by a normal law when n is large. (b) Under the CLT approximation, find a so that P(X > a)- 10
10. (8 poinis) Approximate the sum of the series Σ-, using the 20th partial sum, s20 Round to 4 decimal places. (Use your calculator) a. 2 b. Calculate an upper bound for the error/remainder associated with this approximation (s20) using the formula: R,,「f(x) (a). 20こ 10. (8 poinis) Approximate the sum of the series Σ-, using the 20th partial sum, s20 Round to 4 decimal places. (Use your calculator) a. 2 b. Calculate an upper bound for the error/remainder associated...
10. Solve the initial value problem using Laplace transforms: y'+6y = 8 sin(2t), y(0) = 2
MATLAB help please!!!!! 1. Use the forward Euler method Vi+,-Vi + (ti+1-tinti , yi) for i=0.1, 2, , taking yo-y(to) to be the initial condition, to approximate the solution at 2 of the IVP y'=y-t2 + 1, 0 2, y(0) = 0.5. t Use N 2k, k2,...,20 equispaced timesteps so to 0 and t-1 2) Make a convergence plot computing the error by comparing with the exact solution, y: t (t+1)2 exp(t)/2, and plotting the error as a function of...
584 10 Let L(y) denote the Laplace transform of y. If (f)(s) = and L(9) = what is (f + g)? 81.+2 4+2 Explain your answer indicating the properties of the Laplace transform you are using.
Solve the equation using Laplace transforms: y''+6y'+13y=0 y(0)=2, y'(0)=8
Q4. Laplace Transforms a) (20 points) Solve the differential equation using Laplace transform methods y" + 2y + y = t; with initial conditions y(0) = y(O) = 0 |(s+2) e-*) b) (10 points) Determine L-1 s? +S +1