Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
cody_123
Group Title
\[\lim_{x \rightarrow \infty} \frac{ x^4*\sin \frac{ 1 }{ x }+x^2 }{ 1+\left x \right^3}\]
 2 months ago
 2 months ago
cody_123 Group Title
\[\lim_{x \rightarrow \infty} \frac{ x^4*\sin \frac{ 1 }{ x }+x^2 }{ 1+\left x \right^3}\]
 2 months ago
 2 months ago

This Question is Closed

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
@ganeshie8 ?
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
@mathslover ?
 2 months ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
Yep.. working on it. Did you try using (a^3 + b^3) identity? not sure whether that will work or not.
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
x=1/h and h>0
 2 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
on that x is that a cube? I can't read for some reason. I can click on the code.
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
yes it is a cube
 2 months ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
I suggest you simplify the denominator... use the identity.
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
that mod x will open with minus?
 2 months ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
may be divide numerator and denominator by x^3
 2 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
so since x<0 then x=x and since we have x^3 then we could replace x^3 with (x)^3=x^3 now recall that if u>0 then sin(u)/u>1 see if you can use that here divide both top and bottom by 1/x
 2 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
the some l'hopital could be used :)
 2 months ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.1
for large x \[\Large \frac{ x^4\sin \frac{ 1 }{ x }+x^2 }{ 1+\left x \right^3}\approx \frac{ x^4\sin \frac{ 1 }{ x }+x^2 }{ \left x \right^3}\] \[\Large=\frac{ x^4\sin \frac{ 1 }{ x }+x^2 }{ x^2\left x \right}\] \[\Large=\frac{ x^2\sin \frac{ 1 }{ x }+1 }{ \left x \right}\] \[\Large\approx\frac{ x^2\sin \frac{ 1 }{ x } }{ \left x \right}=\frac{x}{x}x\sin\frac{1}{x}\]
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
we have to write x=1/h and then h>0
 2 months ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.1
as \(x\to \infty\) you then get \((1)\cdot 1=1\)
 2 months ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.1
x to infinity you get what i have above
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
@Zarkon how did u use the approximation in the first step?
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
@ganeshie8 ?
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
@mathslover ?
 2 months ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.1
in my first step I got rid of the 1 since for large x the 1 really contributes almost nothing
 2 months ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.1
and by large x I mean large negative (obviously)
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
@mathslover ?
 2 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I would have done it like this: (but this is because i'm not commander data like zarkon (who knows all because he is a superior being to a human) \[\lim_{x \rightarrow  \infty}\frac{\frac{x^4 \sin(\frac{1}{x})}{\frac{1}{x}}+\frac{x^2}{\frac{1}{x}}}{\frac{1}{\frac{1}{x}}\frac{x^3}{\frac{1}{x}}}\] then use the fact that if u>0 then sin(u)/u>1 it should be pretty easy after this point though.
 2 months ago

sidsiddhartha Group TitleBest ResponseYou've already chosen the best response.3
as xtends to  infinity mod(x)=x now try to put \[x=\frac{ 1 }{ t}\]
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
ya @sidsiddhartha
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
i was thinking that only
 2 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
or i guess you could have just said \[\lim_{x \rightarrow \infty}\frac{x^4 \sin(\frac{1}{x})+x^2}{1x^3}=\lim_{x \rightarrow \infty}\frac{x^3 \frac{\sin(\frac{1}{x})}{\frac{1}{x}}+x^2}{1x^3}\]
 2 months ago

sidsiddhartha Group TitleBest ResponseYou've already chosen the best response.3
dw:1402332193100:dw
 2 months ago

sidsiddhartha Group TitleBest ResponseYou've already chosen the best response.3
do u get it ? @cody_123
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
can u write the intermediate steps too? thanks
 2 months ago

sidsiddhartha Group TitleBest ResponseYou've already chosen the best response.3
dw:1402332508279:dw now just substitute x=(1/t)
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
\[\lim_{x \rightarrow \infty} \frac{ (\frac{ 1 }{ t })^4*\sin(t)+(\frac{ 1 }{ t^2 }) }{1+ \frac{1 }{ t^3 } }\]
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
sorry t>0
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
@sidsiddhartha ?
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
is it correct @sidsiddhartha ?
 2 months ago

sidsiddhartha Group TitleBest ResponseYou've already chosen the best response.3
no x=1/t so dw:1402332969397:dw it will be like this
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
ok @sidsiddhartha then ?
 2 months ago

sidsiddhartha Group TitleBest ResponseYou've already chosen the best response.3
now just try to simplify it little more
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ \frac{ 1 }{ t }*\sin t+t}{ 1+t^3 }\]
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
@sidsiddhartha ?
 2 months ago

sidsiddhartha Group TitleBest ResponseYou've already chosen the best response.3
ya good now can do it :)
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
w8 a second in denominator i should be 1t^3
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
@sidsiddhartha ?
 2 months ago

sidsiddhartha Group TitleBest ResponseYou've already chosen the best response.3
nope its all right now just use limit t tends to 0 (sint/t)=1
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
@sidsiddhartha
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
\[1+\frac{ 1 }{ t^3 }=\frac{ t^31 }{ t^3 }\]
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
so t^31 will come in denominator?
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
@sidsiddhartha ?
 2 months ago

sidsiddhartha Group TitleBest ResponseYou've already chosen the best response.3
dw:1402334075049:dw its not ""
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
oh silly mistake :P
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ \frac{ 1 }{ t }*\sin t+t }{ 1+t^2 }\]
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
@sidsiddhartha ?
 2 months ago

sidsiddhartha Group TitleBest ResponseYou've already chosen the best response.3
it should be (t^3+1)
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
ya in the denominator
 2 months ago

cody_123 Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ t1 }{ t^3+1 }\]
 2 months ago

sidsiddhartha Group TitleBest ResponseYou've already chosen the best response.3
yeah :)
 2 months 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.