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Flashcards
2021-11-25
What is L’Hôpital’s rule used for??
Finding the limit of two functions divided together.
What is $$\lim_{x \to a} \frac{f(x)}{g(x)}$$ equivalent to??
$$ \lim_{x \to a} \frac{f'(x)}{g'(x)} $$
What technique could you use for finding the value of $$\frac{\sin(x)}{x}$$ at $x = 0$??
L’Hôpital’s rule.
What are the conditions for applying L’Hôpital’s rule for $$\lim_{x \to a} \frac{f(x)}{g(x)}$$??
$$ \frac{f(x)}{g(x)} = \frac{0}{0} $$
or
$$ \frac{f(x)}{g(x)} = \frac{\pm \infty}{\pm \infty} $$
How could you find the limit of the product of two functions $f(x)g(x)$ when their product is undefined??
$$ f(x)g(x) \equiv \frac{g(x)}{1/f(x)} \equiv \frac{f(x)}{1/g(x)} $$
and use L’Hôpital’s rule.
How could you evaluate $$\lim_{x \to -\infty} x e^x$$??
$$ \lim_{x \to -\infty} \frac{x}{1/e^x} $$
What do you need to consider when rewriting $f(x)g(x)$ as $\frac{f(x)}{1/g(x)}$ or $\frac{g(x)}{1/f(x)}$ in order to use L’Hôpital’s rule??
Which one has a nicer result when you integrate the top and bottom.
How could you evaluate $\lim e^{f(x)}$??
$$ e^{\lim f(x)} $$
How can you tackle an indeterminate form like $1^\infty$??
Rewrite as $e^{\infty \times \ln 1}$.
How can you tell if a limit doesn’t exist??
Approach it from two different directions and see if you get different answers.
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date: 2021-11-25 16:25
tags:
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- '@?school'
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title: Further Maths - L'Hôpital's Rule