Another Stumper (limits): x^(1/2) (1 + 4x^2 + 2x) / (x^(5/2

[Aduial.Elen]

My friend is having trouble with a math assignment question too.

           (1/2)        2
          x     (1 + 4 x  + 2 x)
  lim     ---------------------
x -> +oo     (5/2)
            x      + 1 + 4 x

Hopefully this will make sense when posted.
__________________________
Edited by stapel -- Reason for edit: restoring multi-line formatting

 

[Aduial.Elen]

Darn, it messed up. Let me try to phrase this:


We are asked to find the limit of a fraction as x approaches infinity. On the top of the fraction is x to the exponent 1/2, multiplied by a bracket containing (1 + 4x^2 + 2x). On the bottom of the fraction is x to the exponent 5/2 + 1 + 4x.

So basically the top looks like this: x^1/2 * (1 + 4x^2 + 2x)

While the bottom looks like this: x^5/2 + 1 + 4x.

Many thanks in advance!

 

[galactus]

You have:

\(\displaystyle \L\\\lim_{x\to\infty}\frac{x^{\frac{1}{2}}+4x^{\frac{5}{2}}+2x^{\frac{3}{2}}}{x^{\frac{5}{2}}+4x+1}\)


Divide top and bottom by \(\displaystyle x^{\frac{5}{2}}\)

Resulting in:

\(\displaystyle \L\\\lim_{x\to\infty}\frac{\frac{1}{x^{2}}+4+\frac{2}{x}}{1+\frac{1}{x^{\frac{5}{2}}}+\frac{4}{x^{\frac{3}{2}}}\)

See the limit?.

 

[Aduial.Elen]

I see the limit from what you did, but I don't understand the very first thing you wrote. Perhaps you interpreted my question wrong?

(It's fixed now in the first post by the way)

 

[galactus]

That's the same thing. I just multiplied thorugh by \(\displaystyle \sqrt{x}\)

 

[Aduial.Elen]

Ok- thanks so much for your help!