Limit as x approaches 2 from the right

[huan.conchito]

$Lim x->2^+ [Sqrt (x-2)] (1/x-1/2)$
Please help I am having trouble taking this limit

 

[dextercioby]

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.

 

[Hurkyl]

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?

 

[huan.conchito]

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

 

[huan.conchito]

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

 

[Hurkyl]

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 $x \in [2, \infty)$.

 

[saltydog]

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

 

[dextercioby]

Ooops,i was thinking about

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

which would have been more interesting...

Daniel.

 

[gulsen]

try to use L HOSPİTAL

 

[dextercioby]

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.

 

[huan.conchito]

are you sure its zero ?

 

[gulsen]

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

 

[dextercioby]

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

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

Daniel.

 

[gulsen]

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

 

[dextercioby]

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.

 

[gulsen]

lan mal i am from turkey

 

[dextercioby]

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.

 

[gulsen]

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

 

[gulsen]

and however if i said hospital its hospital

 

[dextercioby]

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.