Further Maths - L'Hôpital's Rule
Pearson Edexcel Further Mathematics 2022
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Flashcards
The rule and when to apply it
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?
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
\[\lim _ {x \to a} \frac{f(x)}{g(x)}\]
?
or
\[\frac{f(x)}{g(x)} = \frac{\pm \infty}{\pm \infty}\]Indeterminate products and powers
How could you find the limit of the product of two functions $f(x)g(x)$ when their product is undefined?
and use L’Hôpital’s rule.
How could you evaluate
\[\lim _ {x \to -\infty} x e^x\]
?
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 can you tackle an indeterminate form like $1^\infty$?
Rewrite as $e^{\infty \times \ln 1}$.
When a limit doesn’t exist
How can you tell if a limit doesn’t exist?
Approach it from two different directions and see if you get different answers.