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education/math/MATH1210 (calc 1)/Limits.md
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@ -28,7 +28,9 @@ To find this limit if it exists we must perform some mathematical manipulations
If we have a one sided limit of the form $\lim_{x \to a^*} \frac{f(x)}{g(x)}$ $f(x) \to k (k \ne 0)$ and $g(x) \to 0$ as $x \to a$ then:
$$ \lim_{x \to a^*} \frac{f(x)}{g(x)} = \infty \space or \space \lim_{x \to a^*} \frac{f(x)}{g(x)} = -\infty $$
# Limits of the Form $\frac{\infty}{\infty}$
If we have a limit of the form $\lim_{x \to a} \frac{f(x)}{g(x)}$ where both $f(x) \to \infty$ and $g(x) \to \infty$ as $x \to a$ then the limit may or may not exist and is said to be an indeterminate form of type $\frac{\infty}{\infty}$
If we have a limit of the form $\lim_{x \to a} \frac{f(x)}{g(x)}$ where both $f(x) \to \infty$ and $g(x) \to \infty$ as $x \to a$ then the limit may or may not exist and is said to be an indeterminate form of type $\frac{\infty}{\infty}$.
To find the limit if it exists we must perform some algebraic manipulations on the quotient in
# Continuity
A function is continuous if their graph can be traced with a pencil without lifting the pencil from the page.