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Wed 27 Jul, 2005 07:07 pm
Find the limit of the sqrt{x} as x---> positive infinity.
Meh it's summer and unfortunately I tend to forget these things over summmer
But I believe the limit is positive infinity.
Show your work
Once again, please show us your effort on these before asking for help.
Simple to think about: what happens when x gets really, really big? What happens when it gets even bigger? And bigger still?
hey
I posted my work in the first message but accidently deleted the typed work. Okay, the answer is positive infinity but HOW do I know for sure?
Well, really, that doesn't make any sense. What you should be saying is that the limit does not exist. Infinity, since it is not a number, cannot be a limit.
Sqrt(x) isn't a function...
Re: hey
fdrhs wrote:I posted my work in the first message but accidently deleted the typed work. Okay, the answer is positive infinity but HOW do I know for sure?
Because the first derivative of the function is always positive, though it approaches zero as X approaches infinity.
What about the negative roots ?
Both the function and its corresponding derivative have positive and negative roots. However the problem as stated called for X to approach positive infinity, thus excluding the negative roots a priori.
In both cases the limit is infinity: positive in one case negative in the other.
well
I think positive infinity makes more sense since taking the square root of a negative number does not exist.
You can see that
w ≥ ln(w) + 1 for all w > 0 ...[A]
and hence that
sqrt(x) ≥ ln(sqrt(x)) + 1,
or that
sqrt(x) ≥ (1/2)ln(x) + 1 ...
for all x>0 (equality holds if and only if x=1).
The right hand side of the inequality goes to infinity as x goes to infinity.
It implies that sqrt(x) goes to infinity as x (>0) goes to infinity.
(The symbol "≥" means ">=" ,in case it doesn't show on a display.)
Re: well
fdrhs wrote:I think positive infinity makes more sense since taking the square root of a negative number does not exist.
Incorrect -- it is merely a complex number.
You're not taking the square root of a negative number, the square root is the number that is negative.
Ex. - Sqrt(1,000,000) = -1,000, +1,000
1,000,000 then increases to infinity...
Well the limit he's talking about is for a FUNCTION ergo negative answers for roots are "discarded". Also it was correctly mentioned that TECHNICALLY the limit does not exist since infiniti is actually not an anctual number however for all practical purposes positive infinity is the answer.
Wow I can't believe I remember that.
I had thought that it wasn't a function because it fails the vertical line test (I hate thinking about functions that way though), and therefore the limit couldn't be taken, even disregarding the infinity.
But the square root function does NOT fail the vertical line test as it only yields positive answers. Basicallly its like this:
y=root 4
y=2 AND -2
f(x)=root 4
f(x)=2
make sense now?
Got it. The results of the operation are defined within/as a function although the operation by itself is not. I was thinking of the graph. The use of the radical varies depending on whether it is solitary or used in an equation...
Well if you told a graphing calculator to graph it would only be one sided (to the positive side). However if someone said "graph root x" it could be done 2 ways although you should probably use the function of the suare root as mostly, especially in school, we are told to graph functions.
ok
I want to thank all for your help.
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