A community for students.
Here's the question you clicked on:
 0 viewing
morganKING
 2 years ago
lim
t  0 (t(1cos(t))/(t sin(t))
use using the lhoptialrule
morganKING
 2 years ago
lim t  0 (t(1cos(t))/(t sin(t)) use using the lhoptialrule

This Question is Open

yolifuentes67
 2 years ago
Best ResponseYou've already chosen the best response.0*** I am assuming that by (cos 2x  1) you mean [cos(2x)  1] . It's an indeterminate form 0/0 , so you can use L'Hopital's rule (differentiate numerator and denominator separately). [ cos(2x)  1 ] / [ 1  cos(3x) ] lim x > 0 = [  2sin(2x) ] / 3sin(3x) lim x > 0 That is also an indeterminate form 0/0 , so apply L'Hopital's rule again : = [  4cos(2x) ] / 9cos(3x) lim x > 0 = ( 4 / 9)  Here's a zoomedin portion of the graph of f(x) = [ cos(2x)  1 ] / [ 1  cos(3x) ] You can see the graph passing through the point ( 0 , 4/9 )

morganKING
 2 years ago
Best ResponseYou've already chosen the best response.0were did 3x come from

4kec4
 2 years ago
Best ResponseYou've already chosen the best response.0@morganKING i am getting 1 for the limit of this one, but when i graph i am getting f(t)=3, as t approaches 0

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Are you having trouble finding the derivative? That is the only scenario I can see here since it tells you to use lhospital.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1let f(t)=t(1cos(t)) and g(t)=tsin(t) f(0)=0 and g(0)=0 since we have 0/0 we can use l'hopital rule (i think it is much easier to multiply the bottom by 1+sin(t) by whateves; it doesn't say to do that) Do limt>0 (f'/g') since we have f/g=0/0

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Not for your problem you asked about.

morganKING
 2 years ago
Best ResponseYou've already chosen the best response.0yeah the derivative confused me @myininaya but not sure

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1let f(t)=t(1cos(t)) and g(t)=tsin(t) Recall this above f(t)=ttcos(t) f'(t)=(ttcos(t))'=(t)'(tcos(t))' Derivative of t is easy For finding the derivative of tcos(t) you need the product rule. g'(t) is a bit easier to find.

morganKING
 2 years ago
Best ResponseYou've already chosen the best response.0ZZZ dont get this keep on getting 0/0

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1You should not getting 0/0 after differentiating three times.
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.