The X-> represents as x goes to
I've been working on these two problems for some time and cannot get either of them to work. ( I don't know how to use Math HTML so bear with me )
Find the Limit
Problem 1: lim [ (x/x-1) - (1/lnx) ]
x->1
Problem 2: lim [ sqrt(x^2 + x) - x ]
x->inf
I've been working for quite a while. The solution to both problems is 1/2
Dear DocileRaptor,
For the first problem,
When x=1 the numerator and denominator becomes zero. Hence you can use the L'Hospitals rule. Hope you can continue from here.
For the second problem, multiply both the numerator and denominator by, . Then you would be able to use L'Hospital's rule.
Hope this will help you.
Hello Sudharaka,
I suppose I should have posted how far I did get. I got to this step.
However, when I tried using L'Hospital's Rule, I end up with 0/2 which is incorrect. Can you show me a step process of solving this problem?
I'll try that for the second one, multiplying by the reciprocal makes sense.
Dear DocileRaptor,
You are correct. The limit becomes,
Now you can use the L'Hospital's rule(since when x goes to infinity both the numerator and denominator goes to infinity).
But there's an easy method. Divide both the numerator and denominator by x.....
Hope this will help you.
Ah ha! I see now. This is the first day with L'Hospital's Rule.
So using L'Hospital's Rule twice consecutively on
I end up with
(1/x) / (1+ (1/x) ) as X approaches 1 which is equal to 1/2 Can you put that equation into the code so I can see how the code looks? I am learning how to use latex as we speak