Here are the essential concepts you must grasp in order to answer the question correctly.
L'Hôpital's Rule
L'Hôpital's Rule is a method for evaluating limits of indeterminate forms, such as 0/0 or ∞/∞. It states that if the limit of f(x)/g(x) results in an indeterminate form as x approaches a value, then the limit can be found by taking the derivative of the numerator and the derivative of the denominator separately, and then re-evaluating the limit.
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Polynomial Functions
Polynomial functions are expressions that involve variables raised to whole number powers, combined using addition, subtraction, and multiplication. In the given limit, the expression x³ - 3x² + 2 is a polynomial, and understanding its behavior as x approaches a specific value is crucial for limit evaluation, especially when factoring or simplifying the expression.
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Introduction to Polynomial Functions
Limit Evaluation Techniques
Limit evaluation techniques include various methods for finding the limit of a function as it approaches a certain point. These methods can involve direct substitution, factoring, rationalizing, or using L'Hôpital's Rule. In this case, after applying L'Hôpital's Rule, one can also check the limit by substituting the value directly into the simplified expression or by using polynomial long division.
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