Find the first 2 terms of the asymptotic expansions, for large x, of the following integral:
Find thge first 2 terms of the asymptotic expansions, for large x, of the following integral: (d) / eT㎡ log(1 + t2) dt (d) / eT㎡ log(1 + t2) dt
3. Find the asymptotic expansion of (x, p)-| e-"u-pdu, for large values of x 3. Find the asymptotic expansion of (x, p)-| e-"u-pdu, for large values of x
please answer both!!! (1 point) Use the binomial series to find the first 5 nonzero terms of the power series centered at x = 0 for the following function and then give the open interval of convergence for the full power series. 1 f(x) = (5 + x)5 f(x) = + + + + ... + (Give your The open interval of convergence is: answer in interval notation.) (1 point) For the following indefinite integral, find the full power series...
Part 1: Derive the expected value and find the asymptotic distribution. Part 2: Find the consistent estimator and use the central limit theorem b. Derive the expected value of X for the Weibull(X,2) distribution. c. Suppose X,.. .X,~iid Uniffo,0). Find the asymptotic distribution of Z-n(-Xm) max Let X, X, ~İ.id. Exp(β). a. Find a consistent estimator for the second moment E(X"). Use the mgf of X to prove that your estimator is consistent in the case β=2 b. Use the...
(Calculus 1) tan(3x) 1 - 8-21 e-2 Find the derivative of the integral function H (x) = 4+e-21 dt sin(3x)
Find the half-range cosine and sine expansions of the given function, leaving your answers in terms of cos(n π/2) and sin(n π/2) F(x) cos nx n-1 1 sin nx Submit Find the half-range cosine and sine expansions of the given function, leaving your answers in terms of cos(n π/2) and sin(n π/2) F(x) cos nx n-1 1 sin nx Submit
Differentiate the function f(x) = $* V t2 + +5 dt Find the definite integral (4 sint – 2 cos t)dt Find the indefinite integral. / (tan an x – 3)' sec? x dx
Find the following indefinite integral: 122* •2x² + 7x-3 -dx X-2 Find the following indefinite integral: ( (sec(2x) 2x) + tan(2x))dx
(1 point) For the following indefinite integral, find the full power series centered at 2 O and then give the first 5 nonzero terms of the power series and the open interval of convergence. $(t) = /2 2. In(1+x) dx f(t)=C+ n=1 f(t) = C+ + + +... The open interval of convergence is: (Give your answer in interval notation)
2. Suppose X ~ N (μ,5). Find the asymptotic distribution of X(1-X) using A-methods. 3. Let X denote that the sample mean of a random sample of Xi,Xn from a distribution that has pdf Let Y,-VFi(x-1). Note that X = lari Xi- (a) Show that Mx(t) = (ca-tryM f(x) = e-z, x > 0. Find lim+oo My, (t)