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math: first principles over small h

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eggy 2020-10-14 14:57:08 -04:00
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@ -253,6 +253,9 @@ This is known as the **difference quotient**.
The **instantaneous rate of change (IRoC)** at point $P(a, f(a))$ is represented by the slope of the **tangent line ($m_T$)**. The slope of the tangent line can be found by finding the difference quotient with $h$ as a very small value, e.g., $0.001$. The **instantaneous rate of change (IRoC)** at point $P(a, f(a))$ is represented by the slope of the **tangent line ($m_T$)**. The slope of the tangent line can be found by finding the difference quotient with $h$ as a very small value, e.g., $0.001$.
!!! warning
The above method of finding the IRoC should be disregarded in favour of finding the derivative.
### Sequences ### Sequences
A sequence is a **function** with a domain of all positive integers in sequence, but uses subscript notation ($t_n$) instead of function notation ($f(x)$). A sequence is a **function** with a domain of all positive integers in sequence, but uses subscript notation ($t_n$) instead of function notation ($f(x)$).