Use a CAS to plot the function near the point x0 being approached. From your plot guess the value of the limit.
-Provide a short sentence that summarizes the general limit principle given by the formal notation $\lim _ { x \rightarrow a } [ f ( x ) \pm g ( x ) ] = \lim _ { x \rightarrow a } f ( x ) \pm \lim _ { x \rightarrow a } g ( x ) = L \pm M$, given that $\lim _ { x \rightarrow a } f ( x ) = L$ and $\lim _ { x \rightarrow a } g ( x ) = M$.
A) The limit of a sum or a difference is the sum or the difference of the limits.
B) The sum or the difference of two functions is continuous.
C) The limit of a sum or a difference is the sum or the difference of the functions.
D) The sum or the difference of two functions is the sum of two limits.

Question

Quizplus · Accepted Answer

The general limit principle for sums and differences states that when finding the limit of a sum or a difference of two functions as x approaches a certain point (denoted by a), we can take the limit of each function separately and then add or subtract the resulting limits to get the limit of the original sum or difference. This is shown in the formal notation given, and is the principle used to evaluate many limits involving algebraic expressions. Therefore, choice A is the best option as it accurately summarizes this principle.