find whether: integral from neg. infinity to infinity of 1/((e^x)+e^-x) converges or diverges?

Answer 1

compare the integrand wits y=1/x^2
the quotient is x^2/(e^x+e^-x) which is 0.so 1/(e^x+e^-x is smaller than 1/x^2
As the integral of 1/x^2 converges the smaller one also converges.
For x==> + infinity the limit becomes lim x^2/e^x
and for - infinity it becomes lim x^2/e^-x

Answer 2

² 12/[n(n+3)] >= a million/n isn’t real. try it with n=10: LHS=0.0923, RHS=0.a million. in actuality a million/n(n+3)

Answer 3

i'd answer you, but you do not respect people helping you!