A community for students.
Here's the question you clicked on:
 0 viewing
eiya
 2 years ago
evaluate lim (x>0) S(x)/(X^3) if S(x)= int (from 0 to x) sin (0.5*pi*t^2)
eiya
 2 years ago
evaluate lim (x>0) S(x)/(X^3) if S(x)= int (from 0 to x) sin (0.5*pi*t^2)

This Question is Open

Koikkara
 2 years ago
Best ResponseYou've already chosen the best response.1well, it will be helpful, if u could tell us which grade r u in..?

eiya
 2 years ago
Best ResponseYou've already chosen the best response.0no...only applying indeterminate forms and L'hospital's Rule chapter

Koikkara
 2 years ago
Best ResponseYou've already chosen the best response.1well, may take some time...dw:1363454097397:dw

eiya
 2 years ago
Best ResponseYou've already chosen the best response.0i can see yr hardness to write it....appreciate a lot..!

Koikkara
 2 years ago
Best ResponseYou've already chosen the best response.1@Preetha ....posiibility is like she <<can help you.....

Preetha
 2 years ago
Best ResponseYou've already chosen the best response.0Nah. I dont have a clue! Try @klimenkov

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0how is t related to x ?

eiya
 2 years ago
Best ResponseYou've already chosen the best response.0actually there "dt" after the close bracket

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2\[\lim\limits _{x\rightarrow0}\frac{\int\limits _0^x\sin\frac{\pi t^2}2 dt}{x^3}\] When \(x\rightarrow0\), \(\int\limits _0^x\sin\frac{\pi t^2}2 dt\sim\frac{\pi x^3}{6}\), because \(\sin\frac{\pi t^2}2\sim\frac{\pi t^2}{2}\), when \(t\rightarrow0\). So the limit is \(\frac{\pi}{6}\).

eiya
 2 years ago
Best ResponseYou've already chosen the best response.0are you applying fundamental theorem?

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2Lol. I have just read what you wrote above about L'hopital's rule. \(\left(\int\limits _0^x\sin\frac{\pi t^2}2 dt\right)'_x=\sin\frac{\pi x^2}2\) \(\left(\sin\frac{\pi x^2}2\right)'_x=\pi x\cos\frac{\pi x^2}2\) So we have \(\lim\limits _{x\rightarrow0}\frac{\int\limits _0^x\sin\frac{\pi t^2}2 dt}{x^3}=\lim\limits _{x\rightarrow0}\frac{\sin\frac{\pi x^2}2}{3x^2}=\lim\limits _{x\rightarrow0}\frac{\pi x\cos\frac{\pi x^2}2}{6x}=\lim\limits _{x\rightarrow0}\frac{\pi \cos\frac{\pi x^2}2}{6}=\frac \pi 6\), because \(\lim\limits_{x\rightarrow0}\cos\frac{\pi x^2}2=1\).

eiya
 2 years ago
Best ResponseYou've already chosen the best response.0thanks a lot....but im trying to understand the steps..

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2Do you know the L'hopital's rule?

eiya
 2 years ago
Best ResponseYou've already chosen the best response.0a bit...just learnt last month

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2Do you know what is the derivative?

eiya
 2 years ago
Best ResponseYou've already chosen the best response.0nahh...i got it...understand already....

eiya
 2 years ago
Best ResponseYou've already chosen the best response.0yes...i know derivative...

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Welcome to OpenStudy @eiya

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0http://prezi.com/fs3hqdpcopic/anunofficialguidetoopenstudy/ ^ A guide for you to start your journey well in openstudy @eiya
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.