Sure! Let's find the limit of the function [tex]\(7 - 3x\)[/tex] as [tex]\(x\)[/tex] approaches 5.
First, we need to identify the given function:
[tex]\[ f(x) = 7 - 3x \][/tex]
We need to find the limit of [tex]\(f(x)\)[/tex] as [tex]\(x\)[/tex] approaches 5:
[tex]\[ \lim_{x \to 5} (7 - 3x) \][/tex]
To do this, we can simply substitute [tex]\(x = 5\)[/tex] into the function because this is a continuous function and the value will be well-defined:
[tex]\[ f(5) = 7 - 3(5) \][/tex]
Now, carry out the arithmetic inside the parentheses:
[tex]\[ f(5) = 7 - 15 \][/tex]
Finally, we subtract:
[tex]\[ f(5) = -8 \][/tex]
Therefore, the limit is
[tex]\[ \lim_{x \to 5} (7 - 3x) = -8 \][/tex]
So, the result of this limit as [tex]\( x \)[/tex] approaches 5 is [tex]\(-8\)[/tex].
