A community for students.
Here's the question you clicked on:
 0 viewing
frx
 2 years ago
Show, using L'Hopitals rule, that
\[\lim_{x \rightarrow 0} x^{a}lnx = 0\]
for a>0
I started by doing the first derivitive but it didn't help much and doing more derivitives just made it worse, how should i continue?
\[\lim_{x \rightarrow 0} \frac{ d }{dx} x ^{a}lnx = \lim_{x \rightarrow 0} x^{a1}(alnx+1)\]
frx
 2 years ago
Show, using L'Hopitals rule, that \[\lim_{x \rightarrow 0} x^{a}lnx = 0\] for a>0 I started by doing the first derivitive but it didn't help much and doing more derivitives just made it worse, how should i continue? \[\lim_{x \rightarrow 0} \frac{ d }{dx} x ^{a}lnx = \lim_{x \rightarrow 0} x^{a1}(alnx+1)\]

This Question is Closed

alexandercpark
 2 years ago
Best ResponseYou've already chosen the best response.0remember that you can only apply l'hospital rule on specific forms (the only one i remember i 0/0 at the moment.) remember that \[x^a = \ln (e ^{x^a})\]

frx
 2 years ago
Best ResponseYou've already chosen the best response.0I forgot that, so now I should just derivate? So: \[\lim_{x \rightarrow 0} \frac{ d }{ dx} \ln(e ^{x ^{a}})lnx=\lim_{x \rightarrow 0}\frac{ ax ^{a} lnx \ln(e ^{x ^{a}}) }{ x } \] And that is 0/0, and to get the answer should I just continue to derivate?

frx
 2 years ago
Best ResponseYou've already chosen the best response.0It does get really messy to derivate more.. or maybe I shouldn't derivate further?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1351678852308:dw
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.