Limit Calculation with Multiplication Trick?

[gipc]

Hello,

can someone please help me understand how to solve the following limit? I've tried multiplying by sqrt(x)+sqrt(a) but it doesn't seem to do the trick. How do i continue from there?

http://img78.imageshack.us/img78/3595/asdsadassssggg.jpg

 

[justsof]

L'Hôpital's rule does the job here, check http://en.wikipedia.org/wiki/L'Hôpital's_rule , but as I'm not such a fan of L'Hôpital there is usually a way to work yourself around hopital but I don't see it at this moment. Again, use L'Hôpital for an easy way out here!

 

[Mark44]

Hello,

can someone please help me understand how to solve the following limit? I've tried multiplying by sqrt(x)+sqrt(a) but it doesn't seem to do the trick. How do i continue from there?

http://img78.imageshack.us/img78/3595/asdsadassssggg.jpg

The[/URL] two-sided limit doesn't exist, because if x < a, then the denominator is not a real number. The right-side limit exists, though. If you assume that x > a, multiplying numerator and denominator by sqrt(x) + sqrt(a) will get you something that you can evaluate.

 

[justsof]

Ah, took me a while but you should rather multiply nominator and denominator $$(x^{\frac{1}{2}}+a^{\frac{1}{2}})(x+a)$$ so you can REALLY evaluate the limit with ease :)

 

[Mark44]

I repeat - the two-sided limit doesn't exist, so if you get a value for it, your work is wrong.

 

[Mark44]

Ah, took me a while but you should rather multiply nominator and denominator $$x^{\frac{3}{2}}+a^{\frac{3}{2}}$$ so you can REALLY evaluate the limit with ease :)

And how does that work? Are you saying that (x^1/2 - a^1/2)(x^3/2 + a^3/2) gives you something easy to work with? The middle terms do not drop out.

 

[justsof]

You are right, sorry, I meant multiplying by (x+a)(sqrt(x)+sqrt(a)) but didn't think it over.