Limit as x approaches 2 from the right

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In summary, the conversation was about finding the limit of a given expression as x approaches 2 from the right. The initial expression was simplified and it was discussed that the result should be a real number. There was a mention of a potential issue with the domain, but it was determined that the expression was defined and continuous on the given interval. There was also a suggestion to use L'Hospital's rule, but it was not necessary for the given expression. The conversation then shifted to a discussion about the correct spelling of a French mathematician's name and the nationalities of the participants. Ultimately, it was concluded that the important thing was finding the solution to the limit, not the spelling of names.
  • #1
huan.conchito
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[itex]
Lim x->2^+ [Sqrt (x-2)] (1/x-1/2) [/itex]
Please help I am having trouble taking this limit
 
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  • #2
Work on the denominator.Bring that expression to a common denominator and then see whether u can "fix" something with the big fraction's numerator...

Daniel.
 
  • #3
Just to check, you want:

[tex]
\lim_{x \rightarrow 2^+} \sqrt{x-2} \left( \frac{1}{x} - \frac{1}{2} \right)
[/tex]

correct?

What is giving you trouble?
 
  • #4
I simpliefied it to [itex]Lim x->2^+ -Sqrt[x-2]/ 2x [/itex], but that still doesn't help
 
  • #5
yes, when i plug in [itex]2^+[/itex] i can't get a real number
 
  • #6
I don't see the trouble... [itex]\sqrt{2-2}(\frac{1}{2} - \frac{1}{2})[/itex] is a perfectly real number... and there's no issues of domain, because [itex]\sqrt{x-2}[/itex] is defined and continuous on [itex]x \in [2, \infty)[/itex].
 
  • #7
huan.conchito said:
yes, when i plug in [itex]2^+[/itex] i can't get a real number

Huan, I assume you've figured out how to specify a right-handed limit in Mathematica right?

[tex]Limit[\sqrt{x-2}(\frac{1}{x}-\frac{1}{2}),x\rightarrow 2,Direction\rightarrow -1][/tex]

This returns 0
 
  • #8
Ooops,i was thinking about

[tex] \lim_{x\searrow 2}\frac{\sqrt{x-2}}{\frac{1}{x}-\frac{1}{2}} [/tex]

which would have been more interesting...

Daniel.
 
  • #9
try to use L HOSPİTAL
 
  • #10
For what?It's not necessary for mine & it would be incorrect for theirs...

Daniel.

EDIT:And one more thing:It's Guillaume François Antoine,marquis de l'Hôpital.
 
Last edited:
  • #11
are you sure its zero ?
 
  • #12
there is o.o indefiniteness.u can use l hospital
not:full name is not important
 
  • #13
To his limit it's 0 times 0...No indefiniteness.:wink:

Oh,would you like to be called gursen...?

Daniel.
 
  • #14
what did you mean by saying 'Oh,would you like to be called gursen...?'
 
  • #15
U keep mispelling his name.I wonder if the French dude were still alive & were mis-speling your name,would you have liked it??

Daniel.
 
  • #16
lan mal i am from turkey
 
  • #17
Okay,i'm from Romania,our peoples go way back in the middle ages :wink:

But still,in modern French,l'Hôpital is l'Hôpital,okay?

Daniel.
 
  • #18
as i said name is not important.the important thing is the solution
 
  • #19
and however if i said hospital its hospital
 
  • #20
Funny,in the XVII-th century French,there was no circumflex accent in writing,so he'd spell his name l'Hospital ...:wink:

But the French language has evolved...

Daniel.
 

Related to Limit as x approaches 2 from the right

What is the definition of "limit as x approaches 2 from the right"?

The limit as x approaches 2 from the right is the value that a function or sequence approaches as the input (x) gets closer and closer to 2 from values greater than 2. It is denoted as lim x→2⁺ f(x).

How do you determine the limit as x approaches 2 from the right?

To determine the limit as x approaches 2 from the right, you can either plug in values close to 2 from the right side into the function and observe the resulting output, or use algebraic techniques such as factoring, simplifying, or finding common denominators to evaluate the limit.

What is the significance of the limit as x approaches 2 from the right?

The limit as x approaches 2 from the right is important because it helps us understand the behavior of a function or sequence as the input approaches a specific value. It can also be used to determine if a function is continuous at a given point.

Can the limit as x approaches 2 from the right exist even if the function is not defined at x=2?

Yes, the limit as x approaches 2 from the right can exist even if the function is not defined at x=2. This is because the limit is concerned with the behavior of the function as x gets closer and closer to 2 from the right, not necessarily the value of the function at x=2.

What are some common misconceptions about the limit as x approaches 2 from the right?

One common misconception is that the limit must be equal to the value of the function at x=2. This is not always the case, as the limit can approach a different value than the actual function value at that point. Another misconception is that the limit does not exist if the function has a "hole" or removable discontinuity at x=2. The limit can still exist in this case as long as the function approaches the same value from both sides of x=2.

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