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

@@ -10,7 +10,8 @@ Interpreting it, this can be described as the change in $y$ over the change in $
 As the distance between the two points $a$ and $b$ grow smaller, we get closer and closer to the instantaneous velocity of a point. Limits are suited to describing the behavior of a function as it approaches a point.
 
 If we have the coordinate pair $(a, f(a))$, and the value $h$ is the distance between $a$ and another $x$ value, the coordinates of that point can be described as ($(a + h, f(a + h))$. With this info:
-- The slope of the secant line can be described as $
+- The slope of the secant line can be described as $\dfrac{f(a + h) - f(a)}{a + h - a}$, which simplifies to $\dfrac{f(a + h) - f(a)}{h}$. 
+- The slope of the *tangent line* or the *instantaneous velocity* can be found by taking the limit of the above function as the distance ($h$) approaches zero: $\lim_{h \to 0}\dfrac{f(a + h) - f(a)}{h}$ 
 # Line Types
 ## Secant Line
 A **Secant Line** connects two points on a graph.