Anyone can help me ?
QUESTION :
for all x in (0,1), n is Natural number
f_n (x) := max{1/x , n }
find lim f_n (x) when n -> infinity.
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Anyone can help me ?
QUESTION :
for all x in (0,1), n is Natural number
f_n (x) := max{1/x , n }
find lim f_n (x) when n -> infinity.
Do you mean {1/n, n}? If so then you are looking at "max(1/2, 2)", "max(1/3, 3)", "max(1/4, 4)"...:"max{1/1000000, 1000000}", ... What are those numbers? What is the limit as n goes to infinity?
If you really mean {1/x, n} for fixed x it is essentially the same: "max(1/x, 2)", "max(1/x, 3)", "max(1/x 4)"...:"max{1/x 1000000}", where the first number is some fixed finite number.
i had updated the question to make it clear.Quote:
Originally Posted by HallsofIvy
I was interested to know what is the limit function which f_n approaching to .
It's pretty straight forward if you write out a few terms in the sequence of functions.
For x in (0, 1) (in particular for x positive) 1/x> n when x< 1/n. Sofor x< 1/n and
for x> 1/n, In particular,
for all x in (0, 1).
for 0< x<= 1/2,
for 1/2<= x< 1.
for 0< x<= 1/3 and
for 1/3<= x< 1. Do see what is happening? Given any x, there is eventually an integer N> 1/x so for n> N,
.
i see, so we will get f_n(x) -> infinity eventually. Thanks yea.Quote:
Originally Posted by HallsofIvyIt's pretty straight forward if you write out a few terms in the sequence of functions.
For x in (0, 1) (in particular for x positive) 1/x> n when x< 1/n. So