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- Thread starter shamieh
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These things are NOT the same, so you can't "convert" them...Confused on how we go from

\(\displaystyle \frac{1}{^4\sqrt{1 + x}}\) to \(\displaystyle \frac{4}{3}(1 + x)^\frac{3}{4}\)

Can someone please show me step-by-step. I need to see the basic steps.

Thanks in advance.

$\displaystyle \begin{align*} \frac{1}{\sqrt[4]{1 + x}} &= \frac{1}{ \left( 1 + x \right) ^{\frac{1}{4}} } \\ &= \left( 1 + x \right) ^{-\frac{1}{4}} \end{align*}$

It APPEARS though that you are trying to ANTIDIFFERENTIATE (Integrate) this function, which you should be able to do now...

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What on EARTH are you talking about? WHAT is divergent? WHAT are you actually trying to do with this question?Ahh! Thank you!

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And this particular problem would besince you would get \(\displaystyle a^{3/4}\)which isdivergentcorrect?> 1

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The initial question of the problem was

So essentially I had this \(\displaystyle \lim_{a\to\infty} \frac{4}{3}(1 + a)^{3/4} - \frac{4}{3}\) so I'm guessing since it's \(\displaystyle \infty\) in the square root it's always going to keep growing no matter what and be