Certainly! Let's break down the problem step by step.
First, we have the expression:
[tex]\[ 17 \lim _{x \rightarrow -2} -4x \][/tex]
This expression involves a limit as [tex]\( x \)[/tex] approaches [tex]\(-2\)[/tex].
1. Find the Limit:
We need to determine the limit of the function [tex]\(-4x\)[/tex] as [tex]\( x \)[/tex] approaches [tex]\(-2\)[/tex].
To do this, we substitute [tex]\( x = -2 \)[/tex] into the function [tex]\(-4x\)[/tex]:
[tex]\[ -4(-2) = 8 \][/tex]
Therefore:
[tex]\[ \lim_{x \rightarrow -2} -4x = 8 \][/tex]
2. Multiply the Result by 17:
The original problem has a factor of 17 multiplied by the limit we just found. So we need to take the result from our limit calculation and multiply it by 17:
[tex]\[ 17 \times 8 = 136 \][/tex]
Thus, the final result is:
[tex]\[ 17 \lim _{x \rightarrow -2} -4x = 136 \][/tex]
So, the answer is [tex]\( 136 \)[/tex].
