anonymous
  • anonymous
Help.. Prove that lim as x approaches to 0. x^4cos(2/x)=0
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1347737098765:dw|
anonymous
  • anonymous
Look ziz iz a seempl applicashion of limit lohz:|dw:1347737182410:dw|
anonymous
  • anonymous
Now , since \[\lim_{x \rightarrow 0} \cos(x) = 1\]

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anonymous
  • anonymous
yea
anonymous
  • anonymous
And, on the other hand \[\lim_{x \rightarrow 0} x^4 = 0\]
anonymous
  • anonymous
You have the product of those two being (surprise , surprise !) 0
anonymous
  • anonymous
gotch yaa..!!!
anonymous
  • anonymous
thank you!!
anonymous
  • anonymous
Ahh sorry it is 2/x so here is the correct solution:
anonymous
  • anonymous
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
anonymous
  • anonymous
use squeeze theorem
anonymous
  • anonymous
Buut\[|\cos(\frac{2}{x})| \leq 1, alwayz\]
anonymous
  • anonymous
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
anonymous
  • anonymous
|dw:1347737519682:dw|
anonymous
  • anonymous
yea i got it
anonymous
  • anonymous
Medal ?
anonymous
  • anonymous
thank you both!!
anonymous
  • anonymous
Thanks @math456

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