# Limit as x approaches 2 from the right

• huan.conchito
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.
huan.conchito
$Lim x->2^+ [Sqrt (x-2)] (1/x-1/2)$

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.

Just to check, you want:

$$\lim_{x \rightarrow 2^+} \sqrt{x-2} \left( \frac{1}{x} - \frac{1}{2} \right)$$

correct?

What is giving you trouble?

I simpliefied it to $Lim x->2^+ -Sqrt[x-2]/ 2x$, but that still doesn't help

yes, when i plug in $2^+$ i can't get a real number

I don't see the trouble... $\sqrt{2-2}(\frac{1}{2} - \frac{1}{2})$ is a perfectly real number... and there's no issues of domain, because $\sqrt{x-2}$ is defined and continuous on $x \in [2, \infty)$.

huan.conchito said:
yes, when i plug in $2^+$ i can't get a real number

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

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

This returns 0

$$\lim_{x\searrow 2}\frac{\sqrt{x-2}}{\frac{1}{x}-\frac{1}{2}}$$

which would have been more interesting...

Daniel.

try to use L HOSPİTAL

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:
are you sure its zero ?

there is o.o indefiniteness.u can use l hospital
not:full name is not important

To his limit it's 0 times 0...No indefiniteness.

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

Daniel.

what did you mean by saying 'Oh,would you like to be called gursen...?'

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.

lan mal i am from turkey

Okay,i'm from Romania,our peoples go way back in the middle ages

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

Daniel.

as i said name is not important.the important thing is the solution

and however if i said hospital its hospital

Funny,in the XVII-th century French,there was no circumflex accent in writing,so he'd spell his name l'Hospital ...

But the French language has evolved...

Daniel.

## 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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