Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
evaluate lim (x>0) S(x)/(X^3) if S(x)= int (from 0 to x) sin (0.5*pi*t^2)
 one year ago
 one year ago
evaluate lim (x>0) S(x)/(X^3) if S(x)= int (from 0 to x) sin (0.5*pi*t^2)
 one year ago
 one year ago

This Question is Open

KoikkaraBest ResponseYou've already chosen the best response.1
well, it will be helpful, if u could tell us which grade r u in..?
 one year ago

eiyaBest ResponseYou've already chosen the best response.0
no...only applying indeterminate forms and L'hospital's Rule chapter
 one year ago

KoikkaraBest ResponseYou've already chosen the best response.1
well, may take some time...dw:1363454097397:dw
 one year ago

eiyaBest ResponseYou've already chosen the best response.0
i can see yr hardness to write it....appreciate a lot..!
 one year ago

KoikkaraBest ResponseYou've already chosen the best response.1
@Preetha ....posiibility is like she <<can help you.....
 one year ago

PreethaBest ResponseYou've already chosen the best response.0
Nah. I dont have a clue! Try @klimenkov
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
how is t related to x ?
 one year ago

eiyaBest ResponseYou've already chosen the best response.0
actually there "dt" after the close bracket
 one year ago

klimenkovBest 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 \(\frac{\pi}{6}\).
 one year ago

eiyaBest ResponseYou've already chosen the best response.0
are you applying fundamental theorem?
 one year ago

klimenkovBest ResponseYou've already chosen the best response.2
Lol. 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 \(\lim\limits_{x\rightarrow0}\cos\frac{\pi x^2}2=1\).
 one year ago

eiyaBest ResponseYou've already chosen the best response.0
thanks a lot....but im trying to understand the steps..
 one year ago

klimenkovBest ResponseYou've already chosen the best response.2
Do you know the L'hopital's rule?
 one year ago

eiyaBest ResponseYou've already chosen the best response.0
a bit...just learnt last month
 one year ago

klimenkovBest ResponseYou've already chosen the best response.2
Do you know what is the derivative?
 one year ago

eiyaBest ResponseYou've already chosen the best response.0
nahh...i got it...understand already....
 one year ago

eiyaBest ResponseYou've already chosen the best response.0
yes...i know derivative...
 one year ago

mathsloverBest ResponseYou've already chosen the best response.0
Welcome to OpenStudy @eiya
 one year ago

mathsloverBest ResponseYou've already chosen the best response.0
http://prezi.com/fs3hqdpcopic/anunofficialguidetoopenstudy/ ^ A guide for you to start your journey well in openstudy @eiya
 one year ago
See more questions >>>
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.