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

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

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

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

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

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

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

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

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

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

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

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

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

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

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