Provide an appropriate response.
-Let $\lim _ { x \rightarrow 1 } f ( x ) = 7$ and $\lim _ { x \rightarrow 1 } g ( x ) = - 8$. Find $\lim _ { x \rightarrow 1 } \left[ \frac { - 2 f ( x ) - 4 g ( x ) } { 3 + g ( x ) } \right]$.
A) $= \frac { 18 } { 5 }$
B) $- \frac { 26 } { 3 }$
C) $\frac { 46 } { 5 }$
D) 1

Question

Quizplus · Accepted Answer

By the properties of limits, we have$$\lim _ { x \rightarrow 1 } \left[ \frac { - 2 f ( x ) - 4 g ( x ) } { 3 + g ( x ) } \right] = \frac { \lim _ { x \rightarrow 1 } [ - 2 f ( x ) - 4 g ( x ) ] } { \lim _ { x \rightarrow 1 } [ 3 + g ( x ) ] } = \frac { - 2 \lim _ { x \rightarrow 1 } f ( x ) - 4 \lim _ { x \rightarrow 1 } g ( x ) } { 3 + \lim _ { x \rightarrow 1 } g ( x ) } = \frac { - 2 ( 7 ) - 4 ( - 8 ) } { 3 + ( - 8 ) } = \frac { 18 } { 5 }$$

Provide an Appropriate Response lim⁡x→1f(x)=7\lim _ { x \rightarrow 1 } f ( x ) = 7limx→1​f(x)=7

Provide an Appropriate Response $\lim _ { x \rightarrow 1 } f ( x ) = 7$