1. The problem asks for applications of functions, absolute value functions, limits of functions, and derivatives in various fields. 2. Functions model relationships between variables in computer science, physics, engineering, and daily life. For example, in computer science, a function can represent an algorithm's input-output behavior. 3. The absolute value function $f(x) = |x|$ measures distance from zero and is used in engineering to calculate error magnitudes or in physics to find displacement regardless of direction. For example, the absolute value of velocity difference gives speed difference. 4. Limits of functions describe behavior as inputs approach a point, crucial in physics for instantaneous velocity: $$\lim_{\Delta t \to 0} \frac{\Delta s}{\Delta t}$$ where $\Delta s$ is change in position and $\Delta t$ is change in time. 5. Derivatives represent rates of change and are fundamental in physics for velocity and acceleration, in engineering for stress-strain analysis, and in computer science for optimization algorithms. For example, the derivative of position with respect to time gives velocity: $$v(t) = \frac{ds}{dt}$$. 6. In daily life, derivatives help optimize costs or maximize efficiency, such as minimizing fuel consumption by analyzing rate changes. These concepts provide mathematical tools to model, analyze, and solve real-world problems across disciplines.