Vault Of Euclid

Limit of a Rational-Logarithmic Function using L'Hôpital's Rule

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\(\lim_{x\to 1} \frac{x^3 - x^2 + x - 1}{x + \ln x - 1}\)

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What you need first

Evaluating limits by direct substitution
Recognizing indeterminate forms
Basic differentiation rules including the power rule
The derivative of the natural logarithm

What this problem tests

Tests the ability to recognize a 0/0 indeterminate form and correctly apply L'Hôpital's rule by differentiating the numerator and denominator.

This is a standard calculus problem testing the application of L'Hôpital's rule to resolve indeterminate forms.

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