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

1. anonymous

|dw:1347737098765:dw|

2. anonymous

Look ziz iz a seempl applicashion of limit lohz:|dw:1347737182410:dw|

3. anonymous

Now , since $\lim_{x \rightarrow 0} \cos(x) = 1$

4. anonymous

yea

5. anonymous

And, on the other hand $\lim_{x \rightarrow 0} x^4 = 0$

6. anonymous

You have the product of those two being (surprise , surprise !) 0

7. anonymous

gotch yaa..!!!

8. anonymous

thank you!!

9. anonymous

Ahh sorry it is 2/x so here is the correct solution:

10. 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

11. anonymous

use squeeze theorem

12. anonymous

Buut$|\cos(\frac{2}{x})| \leq 1, alwayz$

13. 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

14. anonymous

|dw:1347737519682:dw|

15. anonymous

yea i got it

16. anonymous

Medal ?

17. anonymous

thank you both!!

18. anonymous

Thanks @math456