Final answer:
Differentiation is the process that involves finding the approximate change in the dependent variable when the independent variable changes by a small amount.
Step-by-step explanation:
The process that involves finding the approximate change in the dependent variable when the independent variable changes by a small amount is called Differentiation. It is a fundamental concept in calculus, specifically in the study of derivatives. By finding the derivative of a function, you can determine the rate at which the dependent variable changes with respect to the independent variable.
In this case, you are asked to find the differential dy when x = 3 and dx = 0.1. To do this, substitute the given values into the derivative of the function: dy = 2(0.5 m¯¹)xdx = 2(0.5 m¯¹)(3)(0.1) = 0.3 m¯¹. Therefore, when x = 3 and dx = 0.1, the differential dy is 0.3 m¯¹.