Question

find the convergence of cos(x)/(1+x^4)

Answer 1

i think i know cos(x) is convergence in R, and 1/(1+x^4) convergence interval, and then I multiple both convergence limit part? correct?

Answer 2

if cos(x) convergence is R, but 1/(1+x^4) convergence part isn't R, what we will get for new function convergence interval ? Is R? or is 1/(1+x^4) convergence limit?

Answer 3

what do you mean by convergence?

Answer 4

convergence interval in this function in terms of x expansion

Answer 5

the expansion for \(\displaystyle\frac{1}{1+x^4}\) converges for \(|x|<1\)

Answer 6

so the new convergence interval should be (-1,1) or R? since we know both function convergence, i think we suppose multiple both convergence interval, but cos(x) convergence interval is R

Answer 7

so i 'm little bit confused

Answer 8

you take the intersection of the two intervals

Answer 9

so it should be (-1,1) correct?

Answer 10

yes

Answer 11

thank you!