Provide an appropriate response.
-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 functions.
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 limits.
D) The sum or the difference of two functions is the sum of two limits.

Question

Quizplus · Accepted Answer

The general limit principle states that the limit of a sum or a difference is the sum or the difference of the limits. This is expressed mathematically as $\lim _ { x \rightarrow a } [ f ( x ) \pm g ( x ) ] = \lim _ { x \rightarrow a } f ( x ) \pm \lim _ { x \rightarrow a } g ( x ) = L \pm M$, given that $\lim _ { x \rightarrow a } f ( x ) = L$ and $\lim _ { x \rightarrow a } g ( x ) = M$.

Provide an Appropriate Response lim⁡x→a[f(x)±g(x)]=lim⁡x→af(x)±lim⁡x→ag(x)=L±M\lim _ { x \rightarrow a } [ f ( x ) \pm g ( x ) ] = \lim _ { x \rightarrow a } f ( x ) \pm \lim _ { x \rightarrow a } g ( x ) = L \pm Mlimx→a​[f(x)±g(x)]=limx→a​f(x)±limx→a​g(x)=L±M

Provide an Appropriate Response $\lim _ { x \rightarrow a } [ f ( x ) \pm g ( x ) ] = \lim _ { x \rightarrow a } f ( x ) \pm \lim _ { x \rightarrow a } g ( x ) = L \pm M$