vault backup: 2025-01-21 12:19:38

education/math/MATH1210 (calc 1)/Limits.md

@@ -46,6 +46,15 @@ An elementary function is any function that is defined using:
 	- Composition
 
 A piece-wise function is *not*  considered an elementary function
+
+- If $f$ and $g$ are continuous at a point $x = a$ and $c$ is a constant then the following functions are also continuous at $x = a$
+- If $g$ is continuous at $a$ and $f$ is continuous at $g(a)$, then $f(g(a))$ is continuous at $a$
+- If $f$ is an elementary function and if $a$ is in the domain of $f$, then $f$ is continuous at $a$
+Together, the above theorems tell us that if $a$ is in the domain of an elementary function, then $\lim_{x \to a} f(x) = f(a)$.
+
+# Intermediate Value Theorem
+Let $f$ be a continuous function on the interval ${}
+
 # Definitions
 
 | Term                  | Definition                                                                    |