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

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

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

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

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

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

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.0Theorem 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

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

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

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.0So 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

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