<p>ok i swore i'd never do this, but i'm desperatet....
how does the limit as x approaches 6+ of : </p>
<h2>sqrt(5x^4 +2x)</h2>
<p>x^2</p>
<p>equal the sqrt of 5? i keep getting infinity?</p>
<p>thanks in advance...</p>
<p>my bad. lmiit as x approaches infinity?</p>
<p>no you just plug 6 in the expression and evaluate. it's a trick question, as the expression is defined at 6</p>
<p>if x goes to infinity, the numerator approaches sqrt(5)(x^2).</p>
<p>does that not simplify to infinty?</p>
<p>nope. the numerator, which approaches sqrt(5)(x^2), when divided by x^2, will have the x^2 canceled. so you are left with sqrt5</p>
<p>sorry to keep bothering you, but where did you get the divide by x^2 part? just randomly?</p>
<p>the original problem:</p>
<h2>sqrt(5x^4 +2x)</h2>
<p>x^2</p>
<p>numerator becomes sqrt(5)(x^2)
denominator stays at (x^2)
the x^2 cancel</p>
<p>but isn't the first step to divide both numerator and denominator by the highest power of x (in this case x^2), so the x^2 on the bottom cancels out right away?
or am i totally thinking wrong?</p>
<p>sorry it'll take me an hour.
go ask your math teacher</p>
<p>When the highest powers in an equation are equal, then the leading coefficient will act as the limit. You can ser the highest pwoers to be equal in this expression by tidying it up a bit. You only need to examine the first part...</p>
<h2>sqrt(5x^4+...)</h2>
<pre><code> x^2
</code></pre>
<h2>x^2sqrt(5)+...</h2>
<pre><code> x^2
</code></pre>
<p>So, both the x^2's cancel out leaving you with the sqrt(5) as your answer. This is what Spectrum303 has rather vaguely indicated as well with his uneloquent solution.;)</p>
<p>My eyes beheld a sky one night,
It seems so long ago,
A perfectly painted portrait,
Be-speckled with blue and gold.</p>
<p>As I sit and ponder more,
It strikes me that you were there,
And it was truly your simple beauty,
That gave the stars their perfect glare.</p>
<p>-plagiarized by me.
-dedicated to my ego, which left me a suicidal note (a second one) at 11:58 PM</p>
<p>EAD you reverberate some certain individual on this forum</p>
<p>oooh yea thanks, evil. i didnt even realize they would be equal after the sqrting part. man i feel stupid now.</p>
<p>its square root so when u devide the top its root 5 + 2/x</p>
<p>as x goes to oo, 2/x goes to zero, so it goes to root 5</p>
<p>Spectrum, don't quit your day job.</p>