lebeque dominated convergence thm


by vandanak
Tags: convergence, dominated, lebeque
vandanak
vandanak is offline
#1
Dec1-09, 06:40 AM
P: 18
i got this question in my test i have solved it like this
Lim n->∞∫sin(x/n)/(1+x/n)^ndx integral from 0 to infinity and sin(x/n)/(1+x/n)^n<=e^-x as sin(x/n)<=1 and (1+x/n)^n tends to e^x so we can apply dominated convergence thm as all fn(x) will be less than e^-x so taking limit inside as sin(x/n) tends to zero as n tends to infinity so answer should be 0 well I have not written detailed steps but if my questions is not clear please say it
Is this correct or else how we have to solve it
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
mathman
mathman is offline
#2
Dec1-09, 04:06 PM
Sci Advisor
P: 5,939
Looks all right to me. Suggestion: use punctuation!!!


Register to reply

Related Discussions
Mass-dominated vs. radiation-dominated. Cosmology 5
Cosmology, K=0, Matter dominated, energy density Advanced Physics Homework 0
Dominated Convergence theorem Calculus 3
Why Are Universities Dominated by the Left? Current Events 69