True or False? l'Hôpital's Rule can be applied multiple times to the same limit.

True. l'Hôpital's Rule can be applied multiple times to the same limit, as long as the result continues to be an indeterminate form .

True or False? l'Hôpital's Rule can be used to evaluate limits as x approaches infinity .

True. l'Hôpital's Rule can be used to evaluate limits as x approaches infinity , provided the limit results in an indeterminate form .

IBMathsDPAnalysis & Approaches (AA)HLFlashcards5. CalculusLimits using l'Hôpital's Rule & Maclaurin Series

Limits using l'Hôpital's Rule & Maclaurin Series (DP IB Analysis & Approaches (AA))

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Define the term indeterminate form.

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Define the term indeterminate form.
An indeterminate form is a quotient of the form $\frac{0}{0}$ or $\frac{\pm \infty}{\pm \infty}$ that results from attempting to evaluate a limit.
Such a form does not provide a definitive answer as to what the limit might be.
True or False?
l'Hôpital's Rule can be applied to any limit.
False.
l'Hôpital's Rule can not be applied to any limit.
It can only be applied to the limit of a quotient $\frac{f (x)}{g (x)}$ for which usual limit evaluation techniques return one of the indeterminate forms $\frac{0}{0}$ or $\frac{\pm \infty}{\pm \infty}$ .
What should your first step be when applying l'Hôpital's Rule?
When applying l'Hôpital's Rule, your first step should be to check that the limit of the quotient results in one of the indeterminate forms $\frac{0}{0}$ or $\frac{\pm \infty}{\pm \infty}$ .
Assuming $\lim_{x \to a} \frac{f (x)}{g (x)}$ returns an indeterminate form, what other expression does l'Hôpital's Rule say that limit is equal to?
Assuming $\lim_{x \to a} \frac{f (x)}{g (x)}$ returns an indeterminate form, then l'Hôpital's Rule states that $\lim_{x \to a} \frac{f (x)}{g (x)} = \lim_{x \to a} \frac{f^{'} (x)}{g^{'} (x)}$ (if that second limit exists).
True or False?
l'Hôpital's Rule can be applied multiple times to the same limit.
True.
l'Hôpital's Rule can be applied multiple times to the same limit, as long as the result continues to be an indeterminate form.
True or False?
l'Hôpital's Rule can be used to evaluate limits as x approaches infinity.
True.
l'Hôpital's Rule can be used to evaluate limits as x approaches infinity, provided the limit results in an indeterminate form.
True or False?
Maclaurin series can also be used to evaluate limits for expressions of the form $\frac{f (x)}{g (x)}$ .
True.
Maclaurin series can also be used to evaluate limits for expressions of the form $\frac{f (x)}{g (x)}$ , including cases where the limit initially returns an indeterminate form $\frac{0}{0}$ or $\frac{\pm \infty}{\pm \infty}$ .
The functions $f (x)$ and $g (x)$ are replaced by their Maclaurin series, and algebra is used to simplify the quotient before attempting to evaluate the limit.

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