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

@@ -18,7 +18,14 @@ $$ \lim_{x \to a} f(x) = L $$
 - As $x$ approaches $a$, the output of $f(x)$ draws closer to $L$. In the above notation, $x$ and $a$ are not necessarily equal.
 - When plotted, the hole is located at $(a, L)$.
 # Indeterminate Limits
-If they have a limit of the form $lim_{x \to a} \frac{f(x)}{g(x)}$ where both $f(x) \to 0$ and $g(x) \to 0$ as $x \to a$ then this limit **may or may not** exist
+If they have a limit of the form $lim_{x \to a} \frac{f(x)}{g(x)}$ where both $f(x) \to 0$ and $g(x) \to 0$ as $x \to a$ then this limit **may or may not** exist and is said to be an indeterminate form of type $\dfrac{0}{0}$.
+To find this limit if it exists we must perform some mathematical manipulations on the quotient in order to change the form of the function. Some of the manipulations that can be tried are:
+- Factor or Foil polynomials and try dividing out a common factor.
+- Multiply numerator and denominator by the conjugate of a radical expression
+- Combine fractions in the numerator or denominator of a complex fraction
+
+# Limits of the Form $\frac{k}{0}, k \ne 0$
+
 # Continuity
 A function is continuous if their graph can be traced with a pencil without lifting the pencil from the page.