Hello MHF, please help me how to proof that , the book says that L'Hospital Rule doenst work in this case.

Thanks!

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- October 31st 2012, 07:02 AMChipset3600Proof that \lim_{x->0}\frac{x^2.sin(\frac{1}{x})}{sin(x)}=0
Hello MHF, please help me how to proof that , the book says that L'Hospital Rule doenst work in this case.

Thanks! - October 31st 2012, 07:56 AMTheEmptySetRe: Proof that \lim_{x->0}\frac{x^2.sin(\frac{1}{x})}{sin(x)}=0
- October 31st 2012, 07:57 AMebainesRe: Proof that \lim_{x->0}\frac{x^2.sin(\frac{1}{x})}{sin(x)}=0
I would suggest splitting the fraction in two - we know that the limit of x/sin(x) as x goes to 0 is 1. So that leaves the limit of xsin(1/x). The value of sin(1/x) fluctuates between -1 and 1 as x goes to 0. So the limit of x times that is 0. Hence the answer is 0.

- October 31st 2012, 03:58 PMChipset3600Re: Proof that \lim_{x->0}\frac{x^2.sin(\frac{1}{x})}{sin(x)}=0
wow! understood, I would not find this solution so quickly. Thanks guys :)