Here's the question you clicked on:
hanifah
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
Can we use L'hospital's rule?
Yeah, I tried that first and got a very long/algebraic nightmare.. is it possible to multiply by the conjugate and then us lhr?
lhospital is working for me
all you need is one round and then plug in
remember to treat a as constant
using L'hospital's rule \[\Large \lim _{x\to a}\frac{\frac{2a^3-4x^3}{2(2ax^3-x^4)^\frac{1}{2}}-a\frac{a^2}{3(a^2x)^\frac {2}{3}}}{-\frac{3ax^2}{4(ax^3)^\frac{3}{4}}}=\frac{-a-\frac{a}{3}}{\frac{-3a^3}{4a^3}}=a\]
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!!
-4/3 divided by -3/4 is 16/9
Also I didn't give you the answer because I wanted you to do it yourself. lol.
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
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
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
yes you are write,thats a good idea ,wolfram can help you only if you know ur algebra already,u jus need it for verification and visualisation...we should sharpen ourselves first before we use machines