# 2.9 Small Changes and Approximations

2.9 Small Changes and Approximations

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This is very useful information in determining an approximation of the change in one variable given the small change in the second variable.

Example:
Given that y = 3x2 + 2x – 4. Use differentiation to find the small change in y when x increases from 2 to 2.02.

Solution:
$\begin{array}{l}y=3{x}^{2}+2x-4\\ \frac{dy}{dx}=6x+2\end{array}$

The small change in is denoted by δy while the small change in the second quantity that can be seen in the question is the x and is denoted by δx.