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- Thread starter Yankel
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- #1

- Feb 13, 2012

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Try multiplying numerator and denominator by $x^{2} + x + 1$...Hello,

I need some help with this limit, I have no clue how to do this with the next constraint: No use of L'hopital rule...

Thank you !

[tex]\lim_{x\to1}\frac{sin(x^{3}-1)}{x-1}[/tex]

Kind regards

$\chi$ $\sigma$

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I thought about it, it gives me what's in the sine, however x->1 and not x->0, so I am still stuck...Try multiplying numerator and denominator by $x^{2} + x + 1$...

Kind regards

$\chi$ $\sigma$

- Feb 13, 2012

- 1,704

$\displaystyle \lim_{x \rightarrow 1} \frac{\sin (x^{3}-1)}{x-1} = \lim_{x \rightarrow 1} \frac{\sin (x^{3}-1)}{x^{3}-1}\ (x^{2} + x + 1)$I thought about it, it gives me what's in the sine, however x->1 and not x->0, so I am still stuck...

... and now what is $\displaystyle \lim_{x \rightarrow 1} \frac{\sin (x^{3}-1)}{x^{3}-1}$?...

... and what is $\displaystyle \lim_{x \rightarrow 1} x^{2} + x + 1$?...

Kind regards

$\chi$ $\sigma$

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