Final answer:
The limit of f(x) as x approaches 0 being equal to f(0) is true if f(x) is continuous at x = 0 and particularly true for a horizontal line or a constant function within the given domain. For the provided case, the limit equals f(0). Linear displacement over time implies zero acceleration.
Step-by-step explanation:
The statement lim x -> 0 f(x) = f(0) can be either true or false depending upon the function f(x). Generally, this statement represents the limit of a function as x approaches zero. However, to say this is always true would be incorrect because the limit will equal f(0) if and only if f(x) is continuous at x = 0.
Since you have described a horizontal line, we can understand that f(x) is constant for all values of x in the specified domain (0 ≤ x ≤ 20). For a constant function, f(x) would have the same value at all points, including x = 0. Therefore, in this specific case, the limit would indeed be equal to f(0). The statement is true for the given function.
Regarding the continuous probability function, P (0 < x < 12), if f(x) is constant over the interval, then the probability P is 1 for all x in the interval (0 < x < 12). Lastly, if a plot of displacement versus time is linear with a constant slope, the acceleration is indeed zero because acceleration would be the second derivative of the position function, which would be zero for a linear function