When using L'Hospital's rule, do you take the derivative of the problem? Or do you put the derivative of the denominator over the derivative of the numerator. For example: does $\frac{\ln(9-4x)}{\tan(x-2)}$ become $\frac{\frac{-4}{9-4x}}{\sec^2(x-2)}$ or do you need to use the quotient rule?
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3$\begingroup$ No quotient rule $\endgroup$– FomalhautNov 24, 2019 at 20:57
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2$\begingroup$ $\lim \frac{u(x)}{v(x)} = \lim \frac{u'(x)}{v'(x)}$ is what you do $\endgroup$– fGDu94Nov 24, 2019 at 21:01
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2 Answers
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From @GeorgeDewhirst: $\lim \frac{u(x)}{v(x)} = \lim \frac{u'(x)}{v'(x)}$ is what you do.
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Others have already given the answer - $\lim \frac{u(x)}{v(x)} = \lim \frac{u'(x)}{v'(x)}$ is correct - but you should think more about why.
Remember what a limit is - what the value of a function approaches. If the function approaches an indeterminate form, such as $\frac{0}{0}$, then it is useful to consider the relative rate of change of numerator and denominator, since this difference is important in evaluating forms such as $\frac{0}{0}$. And instantaneous rate of change is just the derivative.
