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anonymous
 3 years ago
lim
t  0 (t(1cos(t))/(t sin(t))
use using the lhoptialrule
anonymous
 3 years ago
lim t  0 (t(1cos(t))/(t sin(t)) use using the lhoptialrule

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anonymous
 3 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 )

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

anonymous
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1Not for your problem you asked about.

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

myininaya
 3 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.

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

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