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math456
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Help.. Prove that lim as x approaches to 0. x^4cos(2/x)=0
 one year ago
 one year ago
math456 Group Title
Help.. Prove that lim as x approaches to 0. x^4cos(2/x)=0
 one year ago
 one year ago

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math456 Group TitleBest ResponseYou've already chosen the best response.0
dw:1347737098765:dw
 one year ago

Mikael Group TitleBest ResponseYou've already chosen the best response.0
Look ziz iz a seempl applicashion of limit lohz:dw:1347737182410:dw
 one year ago

Mikael Group TitleBest ResponseYou've already chosen the best response.0
Now , since \[\lim_{x \rightarrow 0} \cos(x) = 1\]
 one year ago

Mikael Group TitleBest ResponseYou've already chosen the best response.0
And, on the other hand \[\lim_{x \rightarrow 0} x^4 = 0\]
 one year ago

Mikael Group TitleBest ResponseYou've already chosen the best response.0
You have the product of those two being (surprise , surprise !) 0
 one year ago

math456 Group TitleBest ResponseYou've already chosen the best response.0
gotch yaa..!!!
 one year ago

math456 Group TitleBest ResponseYou've already chosen the best response.0
thank you!!
 one year ago

Mikael Group TitleBest ResponseYou've already chosen the best response.0
Ahh sorry it is 2/x so here is the correct solution:
 one year ago

Mikael Group TitleBest ResponseYou've already chosen the best response.0
Theorem we all can use states that Product of a Bounded function by another function that tends to zero  also tends to ZERO in the same limit
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.2
use squeeze theorem
 one year ago

Mikael Group TitleBest ResponseYou've already chosen the best response.0
Buut\[\cos(\frac{2}{x}) \leq 1, alwayz\]
 one year ago

Mikael Group TitleBest ResponseYou've already chosen the best response.0
So we do have true the required assumptions: One of the factors (i.e. cos 2/x) is a bounded function while the other factor : x^4 tends to 0 when x>0
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.2
dw:1347737519682:dw
 one year ago

math456 Group TitleBest ResponseYou've already chosen the best response.0
yea i got it
 one year ago

math456 Group TitleBest ResponseYou've already chosen the best response.0
thank you both!!
 one year ago

Mikael Group TitleBest ResponseYou've already chosen the best response.0
Thanks @math456
 one year ago
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