Limit as x approaches 2 from the right

1. Apr 6, 2005

huan.conchito

$Lim x->2^+ [Sqrt (x-2)] (1/x-1/2)$

2. Apr 6, 2005

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.

3. Apr 6, 2005

Hurkyl

Staff Emeritus
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?

4. Apr 6, 2005

huan.conchito

I simpliefied it to $Lim x->2^+ -Sqrt[x-2]/ 2x$, but that still doesnt help

5. Apr 6, 2005

huan.conchito

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

6. Apr 6, 2005

Hurkyl

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

7. Apr 6, 2005

saltydog

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

8. Apr 6, 2005

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.

9. Apr 6, 2005

gulsen

try to use L HOSPİTAL

10. Apr 6, 2005

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.

Last edited: Apr 6, 2005
11. Apr 6, 2005

huan.conchito

are you sure its zero ?

12. Apr 6, 2005

gulsen

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

13. Apr 6, 2005

dextercioby

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

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

Daniel.

14. Apr 6, 2005

gulsen

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

15. Apr 6, 2005

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.

16. Apr 6, 2005

gulsen

lan mal i am from turkey

17. Apr 6, 2005

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.

18. Apr 6, 2005

gulsen

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

19. Apr 6, 2005

gulsen

and however if i said hospital its hospital

20. Apr 6, 2005

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.