# Can Math Prove Lim f(x)*g(x) Convergence/Divergence?

• Dell
In summary, the conversation discusses the convergence of a limit involving the product of two functions and the mathematical proof for it. It is concluded that nothing can be said about the convergence of the limit of f(x)*g(x), while the limit of f(x)+g(x) is proven to diverge.

#### Dell

if i have a lim of f(x)*g(x) can i say it is limf(x)*limg(x) like i could if i had lim of f(x)+g(x),
more specifically, in my homework i have a question where,

lim f(x) converges
x->inf

lim g(x) diverges
x->inf

1) u(x)=f(x)+g(x)
2) u(x)=f(x)*g(x)

for 1) i say
lim f(x)+g(x)= lim f(x) + lim g(x)====> diverges

for 2) I am not sure, but i think
if f(X) converges to any number, K*inf=inf and u(x) diverges
if f(X) converges to 0 , then 0*inf is undefined and u(x) diverges

1st of all i am not 100% that i am right, second of all how do i prove this MATHEMATICALLY?

Dell said:
lim f(x) converges
x->inf

lim g(x) diverges
x->inf

2) u(x)=f(x)*g(x)

Hi Dell!

(have an infinity: ∞ )

Hint: x -> ∞ for f(x) = 1/x2, g(x) = x3 ?

x -> ∞ for f(x) = 1/x2, g(x) = x ?

in that case it really does diverge, but can i do that, just take any 2 functions and see what happens with them?? surely that is just one example and not enough to prove anything

o i see what you are saying, you are DISPROVING what i said,
so what does this mean? tha nothing can be said about fx*gx?? was i right about fx+gx??

Dell said:
o i see what you are saying, you are DISPROVING what i said,
so what does this mean? tha nothing can be said about fx*gx?? was i right about fx+gx??

Yes and yes