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Can i slit up lims

  • Thread starter Dell
  • Start date
  • #1
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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

and i am asked about convergence of lim u(x) when
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) im 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?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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lim f(x) converges
x->inf

lim g(x) diverges
x->inf

and i am asked about convergence of lim u(x) when

2) u(x)=f(x)*g(x)
Hi Dell! :smile:

(have an infinity: ∞ :wink:)

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

x -> ∞ for f(x) = 1/x2, g(x) = x ? :wink:
 
  • #3
590
0
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
 
  • #4
590
0
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??
 
  • #5
tiny-tim
Science Advisor
Homework Helper
25,832
249
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 :wink:
 

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