diff --git a/docs/mhf4u7.md b/docs/mhf4u7.md index 6dbd0f9..eea6128 100644 --- a/docs/mhf4u7.md +++ b/docs/mhf4u7.md @@ -389,6 +389,17 @@ Therefore, a function is only continuous at $a$ if all of the following are true - $\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x)$ - $\lim_{x \to a} f(x) = f(a)$ +### Limits approaching infinity + +As $x$ approaches infinity, $\lim_{x \to ∞} f(x)$ has only three possible answers. + +By dividing both sides of a fraction by the $x$ variable of the highest degree, if $m$ is the degree of the denominator and $n$ is the degree of the numerator: + + - If $m > n$, $\lim_{x \to ∞} f(x) = 0$ + - If $m < n$, $\lim_{x \to ∞} f(x) = ± ∞$ + - The sign of infinity can be found by evaluating the limit + - If $m = n$, $\lim_{x \to ∞} f(x) = \frac{a}{b}$, where $a$ and $b$ are the coefficients of the degree of the numerator and the denominator, respectively. + ## Resources - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)