(B) Let {fn(x)}ı = {xlnx. cos(x –1)"}1 be a sequence of meaurable functions defined over [1,2]. Show that: (a) {fn(x)}=1 converges to a function f(x) to be determined. (b) Show that fn(x) is dominated by some integrable function for all n. Then apply the dominated convergence theorem %3D In=1 2 to evaluate Lim x In r.cos(x - 1)" dµ . n 00

(B) Let {fn(x)}ı = {xlnx. cos(x –1)"}1 be a sequence of meaurable functions defined over [1,2]. Show that: (a) {fn(x)}=1 converges to a function f(x) to be determined. (b) Show that fn(x) is dominated by some integrable function for all n. Then apply the dominated convergence theorem %3D In=1 2 to evaluate Lim x In r.cos(x - 1)" dµ . n 00

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

a) is f(x) = x3sin(1/x) uniformly continuous at (0,2] b) is g(x) = ln(x2+2) uniformly continuous at (-infinity, infinity) c) Decide if f(x) = x4sin(1/x3) is uniformly continuous at f : (0, infinity) --> R
Determine the convergence of the improper integral sin(7-6x) dx. (A) converges to 7 (B) converges to 1 (C) diverges, the limit tends to ∞ (D) diverges, the limit DNE (E) converges to 0 (F) diverges, the limit tends to -
f(x) is continuous on (-∞,00). Use the given information to sketch the graph of f. f'(x) f''(x) + + 0 -3 -2.5 + + 0 - +0 5 1 X f(x) | 7.9 3.7 0 -2.7 -3.8 -7.9 -5 -2.5 0 5 0 6
5. Let (n) be a uniformly bounded sequence of functions which are Riemann integrable on [a, b, and put 岔 F, (r) =Jf" (t)dt for a $15 b. 2 Show that there exists a subsequence {Fn^1 which converges uniformly on [a, b
The Ramos family combined annual income is 850,000 pesos last year, This Year, the said amount increased by an additional 150,000 pesos. Find the ratio of Ramos Family's combined annual income for this year compared last year.