Evaluating Limits using L'Hospital (2)

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SUMMARY

The limit evaluation using L'Hôpital's Rule for the expression $$\frac{x^4 - 3x^3 + 3x^2 - x}{x^4 - 2x^3 + 2x - 1}$$ as x approaches 1 reveals that the initial incorrect result of $$\frac{0}{6}$$ was due to improper application of derivatives. After applying L'Hôpital's Rule three times and correcting the derivative calculations, the correct limit is confirmed to be $$\frac{1}{2}$$. The discussion emphasizes the importance of showing work to identify errors in limit evaluations.

PREREQUISITES
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  • Familiarity with limit evaluation techniques
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Students and educators in calculus, mathematicians focusing on limit evaluations, and anyone seeking to improve their understanding of L'Hôpital's Rule and its applications.

shamieh
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lim x--> 1
$$
\frac{x^4 - 3x^3 + 3x^2 - x}{x^4 - 2x^3 + 2x - 1}$$I got $$\frac{0}{6} = 0$$
 
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That's incorrect. Since you showed no work, I can't tell you where you went wrong. I will tell you I applied L'Hôpital's Rule 3 times to get the value of the limit.
 
re did the problem, didn;t take the deriv properly in the denom. Did you get $$\frac{-1}{4}$$
 
No, that's no what I got either (and I verified my result using a CAS). If you show your work, I can address where you are going wrong. :D
 
wow I'm a idiot. I put 24 - 12 = 24... -_-... I got $$\frac{1}{2}$$ .. correct?
 
shamieh said:
wow I'm a idiot. I put 24 - 12 = 24... -_-... I got $$\frac{1}{2}$$ .. correct?

Yes, that's correct.
 

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