Final answer:
The linear approximation of the function f(h) = h near h = 25 is simply the function itself, f(h) = h, as it is already a linear function. For the horizontal line function f(x)=20 within the interval 0 ≤ x ≤ 20, it is a horizontal line segment lying within that domain on the x-axis. Without specific functions for further approximations, no precise answers can be given.
Step-by-step explanation:
To obtain a linear approximation of the function f(h) = h near h = 25, we need to recognize that this is a very simple case because f(h) = h is already a linear function. The slope of this function is 1, and there is no y-intercept since it passes through the origin. Therefore, near any point, including h = 25, the linear approximation would simply be the function itself, f(h) = h.
For additional linear approximations mentioned in the question, not enough information is provided to create the approximations unless assuming the small-angle approximation where tan(θ) ≈ θ could be applied. For example, using that approximation near small angles in a function involving trigonometry might simplify the expression but without the specific function, no precise approximation can be given.
Considering the function f(x) = 20 for 0 ≤ x ≤ 20, the function represents a horizontal line at y = 20. Since it's restricted to the domain 0 ≤ x ≤ 20, the line segment would lie within that interval on the x-axis.