Today we discussed an algebraic method for evaluating 0/0 or infinity/infinity indeterminate limits. The method is called L'Hospital's Rule. If, as x-->a, our original limit of f(x) / g(x) approaches 0/0 or inf/inf, find the derivatives of the numerator and denominator separately (what many people WISH the quotient rule would be)and then let x--> a in this new ratio of the derivatives. If we get an answer for this limit, the number we get is the correct limit for the original limit. Understanding why "L'Hop" works involves using the Mean value Theorem with parametric position functions.
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Today we discussed an algebraic method for evaluating 0/0 or infinity/infinity indeterminate limits. The method is called L'Hospital's Rule.
If, as x-->a, our original limit of
f(x) / g(x) approaches 0/0 or inf/inf, find the derivatives of the numerator and denominator separately
(what many people WISH the quotient rule would be)and then let x--> a in this new ratio of the derivatives. If we get an answer for this limit, the number we get is the correct limit for the original limit.
Understanding why "L'Hop" works involves using the Mean value Theorem with parametric position functions.
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