## hanifah one year ago if a>0 what is the lim(x->a) ((sqrt(2xa^3 - x^4)) - a(cuberoot((a^2)(x))))/(a-(ax^3)^(1/4)) What method can help simplify this better? I started by multiplying top and bottom by the conjugate and it was still pretty messy. equation attached in comments for clarity. Any help would be appreciated! thanks

1. hanifah

2. myininaya

Can we use L'hospital's rule?

3. hanifah

Yeah, I tried that first and got a very long/algebraic nightmare.. is it possible to multiply by the conjugate and then us lhr?

4. myininaya

lhospital is working for me

5. myininaya

all you need is one round and then plug in

6. myininaya

remember to treat a as constant

using L'hospital's rule $\Large \lim _{x\to a}\frac{\frac{2a^3-4x^3}{2(2ax^3-x^4)^\frac{1}{2}}-a\frac{a^2}{3(a^2x)^\frac {2}{3}}}{-\frac{3ax^2}{4(ax^3)^\frac{3}{4}}}=\frac{-a-\frac{a}{3}}{\frac{-3a^3}{4a^3}}=a$

8. hanifah

ahhh, so I got the derivatives correct, but I simplified to something that is i don't even know.. haha. honest mistake that will probably kill me on the final=/.. giving the medal to @Jonask this round sorry @myininaya i appreciate the help though!!

9. myininaya

-4/3 divided by -3/4 is 16/9

10. myininaya

Also I didn't give you the answer because I wanted you to do it yourself. lol.

11. hanifah

i know.. @myininaya i'm guessing you're a teacher? haha joking.. jonask doesn't have a medal also I'm not entirely sure what the rules of openstudy are.. i just ask questions, but i feel like some people take the medals pretty seriously. I will sleep on it and get back to you :P

12. myininaya

No I don't care about the medals. I just want the students to be able to get the answers themselves. This isn't suppose to be a site when you can come to cheat.

yes ...the answer shud be 16a/9...since this was a messy job i decided to write the solution wich u obviously attemted...hence u cud see your mistake

14. hanifah

agree, i couldn't figure out where i messed up via wolfram so open study is the next best thing. i need to improve my algebra