Limit evaluation. (Please confirm my work)

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SUMMARY

The limit evaluation discussed is \lim_{x \to 2}\,\frac{x^3-4x^2+7x-6}{x-2}, which simplifies to the polynomial x^2-2x+3 after synthetic division. Evaluating this polynomial at x=2 yields a final answer of 3. Additionally, L'Hopital's rule is suggested as an alternative method for verification, although the user is not yet familiar with it.

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  • Familiarity with L'Hopital's rule (optional)
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  • Learn about evaluating limits in calculus
  • Explore L'Hopital's rule for indeterminate forms
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mateomy
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Evaluate:

<br /> \lim_{x \to 2}\,\frac{x^3-4x^2+7x-6}{x-2}<br />


To evaluate this limit did some synthetic division to ultimately get the polynomial of
<br /> x^2-2x+3<br />

and evaluating this as as x\to2 I ended up with a final answer of 3.

Can someone just confirm that this is in fact, the correct answer. I have nothing to check my work with and I am just making sure all my skills are in order before my final.

Thank you very much in advance.
 
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Yes, this is correct. You could also use L'Hopital's rule to check, if you know about that.
 
Awesome thanks. No, not quite at L'Hopital yet, next semester.
 

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