Here are the essential concepts you must grasp in order to answer the question correctly.
Limit of a Function
The limit of a function describes the value that a function approaches as the input approaches a certain point. In this case, we are interested in the behavior of the functions f(x), g(x), and h(x) as x approaches 1. Understanding limits is fundamental in calculus as it lays the groundwork for continuity, derivatives, and integrals.
Recommended video:
Limits of Rational Functions: Denominator = 0
Limit Laws
Limit laws are a set of rules that allow us to compute limits of functions based on the limits of their components. For example, the limit of the difference of two functions is the difference of their limits, which is expressed as lim x→c (f(x) - g(x)) = lim x→c f(x) - lim x→c g(x). These laws simplify the process of finding limits and are essential for solving limit problems.
Recommended video:
Difference of Limits
The difference of limits states that if the limits of two functions exist as x approaches a certain value, then the limit of their difference also exists. Specifically, if lim x→c f(x) = L and lim x→c g(x) = M, then lim x→c (f(x) - g(x)) = L - M. This concept is crucial for solving the given limit problem involving f(x) and g(x).
Recommended video: