Further Maths - L'Hôpital's Rule
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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
\[\frac{f(x)}{g(x)} = \frac{\pm \infty}{\pm \infty}\]What is \(\lim _ {x \to a} \frac{f(x)}{g(x)}\) equivalent to?
\[\lim _ {x \to a} \frac{f'(x)}{g'(x)}\]
How could you evaluate
\[\lim _ {x \to -\infty} x e^x\]??
\[\lim_{x \to -\infty} \frac{x}{1/e^x}\]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 \(\lim _ {x \to -\infty} x e^x\)?
\[\lim _ {x \to -\infty} \frac{x}{1/e^x}\]