What is (x+y)^(2/3)?

Question

ganeshie8 · Answer

$\large  (x+y)^{\frac{2}{3}} $

ganeshie8 · Answer

$\large  [(x+y)^2]^{\frac{1}{3}} $

ganeshie8 · Answer

$\large  \sqrt[3]{(x+y)^2} $

ganeshie8 · Answer

is that wat u looking for ?

anonymous · Answer

Can you expand it?

ganeshie8 · Answer

oh binomial expansion !

anonymous · Answer

To clarify, how would you expand (x+y)^(2/3)?

anonymous · Answer

To solve Lim h--> 0 (f(a+h)-f(a))/h for f(x) = x^(2/3)?

ganeshie8 · Answer

ahh that should be easy, 

$\large  \lim \limits_{h \to 0} \frac{(x+h)^\frac{2}{3}-x^{\frac{2}{3}}}{h}$

ganeshie8 · Answer

like that ?

anonymous · Answer

Yes! But then how would you expand (x+h)^(2/3)?

anonymous · Answer

If you don't use the limit way, how can I prove f(x) is differentiable at every point on (0,1) for the mean value theorem?

anonymous · Answer

f(x) refers to x^(2/3)

ganeshie8 · Answer

not sure, sorry :(

agent0smith · Answer

Yeah i tried and gave up. Wolfram alpha used l'hopitals rule to solve it, idk if there's a way to simplify that.

anonymous · Answer

I do know l'hopitals but we didn't learn it in class yet so it's not allowed. I think I'll just use agent0smith's way of showing x in (0,1) is valid for f'(x)

anonymous · Answer

What is the degree of (1/x)-((x+1)/2x)?

agent0smith · Answer

degree usually refers to polynomials... I guess that would be degree zero if you really needed the degree, since (x+1)/2x = x/2x + 1/2x and x/2x = 2.

But i don't see why you'd want the degree of that...

anonymous · Answer

My teacher wanted us to find it. Sometimes, he asks us questions that have no answers to make us think. Maybe this is one of them? 
No wonder my math hw is taking so long...

agent0smith · Answer

I think you'd just say it's not a polynomial. Rational functions don't have a degree.

anonymous · Answer

Good answer! How long will you be online today? Your math is really good!

agent0smith · Answer

Well i have a degree in maths and physics and i'm a precalculus/algebra 2/AP physics teacher :D i'll be online a bit longer

anonymous · Answer

You're teaching so many subjects! And you're def the most patient teacher on this website!

agent0smith · Answer

yeah i teach four total... a physics class in addition to AP physics.

anonymous · Answer

wow, that's a lot of grading...

anonymous · Answer

are you online everyday?

agent0smith · Answer

Yeah, pretty much every day :)

anonymous · Answer

That's awesome!