shamieh said:wow I'm a idiot. I put 24 - 12 = 24... -_-... I got \(\displaystyle \frac{1}{2}\) .. correct?
L'Hospital's rule is a mathematical theorem that helps in evaluating limits of indeterminate forms. It states that if both the numerator and denominator of a fraction approach 0 or infinity, then the limit of the fraction is equal to the limit of the derivative of the numerator divided by the derivative of the denominator.
The conditions for using L'Hospital's rule are that the limit must be in an indeterminate form (0/0 or infinity/infinity), the limit must be a fraction, and the function must be differentiable in a neighborhood of the limit point.
Yes, L'Hospital's rule can be used for evaluating limits at infinity. In this case, the limit will be in the form of infinity/infinity, and the same rule of taking the derivative of the numerator and denominator still applies.
Yes, there are limitations to using L'Hospital's rule. It can only be used for limits of indeterminate forms, and it may not always provide the correct answer. In some cases, it may lead to an incorrect result or an infinite loop of derivatives.
Yes, L'Hospital's rule can be used for evaluating limits of trigonometric functions. However, the limit must be in an indeterminate form and the function must be differentiable in a neighborhood of the limit point.