L'Hopital's Rule for evaluating limits from "summary" of Differential Calculus by S Balachandra Rao
L'Hopital's Rule for evaluating limits is an important tool in calculus that allows us to evaluate limits of certain indeterminate forms. These indeterminate forms arise when we have limits that result in expressions like 0/0 or infinity/infinity, which are not immediately solvable using direct substitution. The rule states that if we have a limit of the form f(x)/g(x) as x approaches a certain value, and both f(x) and g(x) approach 0 or infinity as x approaches that value, then the limit of the ratio is equal to the limit of the ratio of the derivatives of f(x) and g(x) as x approaches the same value. In other words, we can differentiate the numerator and the denominator separately and then take the limit of the resulti...
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