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EvLer
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I was just wondering... it is used when the limit is of indetermined form: 0/0 or inf/inf, but is it valid to apply it to a "regular" limit? technically it seems to give the same answer...
Yes, L'Hospital's rule is only valid for "regular" limits, which are limits where both the numerator and denominator approach a constant value as the independent variable approaches a specific value.
The purpose of L'Hospital's rule is to simplify the evaluation of indeterminate forms (such as 0/0 or ∞/∞) in calculus by finding the limit of the ratio of the derivatives of the numerator and denominator.
Yes, L'Hospital's rule can be used for limits involving trigonometric functions as long as the limit is in the form of 0/0 or ∞/∞ and both the numerator and denominator are differentiable.
Yes, L'Hospital's rule cannot be used to evaluate limits that do not approach a constant value, such as limits that approach infinity or negative infinity. It also cannot be used for limits involving complex numbers or limits involving functions with discontinuities.
Yes, L'Hospital's rule can be applied multiple times as long as the resulting limit is still in indeterminate form. However, it is important to note that blindly applying L'Hospital's rule multiple times may lead to incorrect results, so it should be used with caution.