Final answer:
L'Hôpital's Rule is a mathematical technique used to evaluate limits involving indeterminate forms. It states that if a limit of the form 0/0 or ∞/∞ is encountered, and taking the derivative of both the numerator and denominator still results in an indeterminate form, then the limit can be evaluated using the derivative of the numerator divided by the derivative of the denominator. The principle of L'Hôpital's Rule is a mathematical technique used to evaluate limits involving indeterminate forms.
Step-by-step explanation:
Indeterminate forms are expressions where the value of the limit is not immediately evident. The rule states that if a limit of the form 0/0 or ∞/∞ is encountered, and taking the derivative of both the numerator and denominator still results in an indeterminate form, then the limit can be evaluated using the derivative of the numerator divided by the derivative of the denominator.
For example, if we have the limit as x approaches 0 of (sin x) / x, we can use L'Hôpital's Rule. Taking the derivatives of both the numerator and denominator gives us cos x / 1, which evaluates to 1 at x = 0. Therefore, the limit of (sin x) / x as x approaches 0 is 1.