Answer :
To find the limit of the function \( f(x) \) as \( x \) approaches 5, we need to understand the behavior of the function \( f(x) \) at that particular point. Suppose we have the function \( f(x) = 2x + 3 \).
Here are the steps to solve for the limit:
1. Substitute the value of \( x \): The first step in finding the limit is to directly substitute the value \( x = 5 \) into the function \( f(x) \).
2. Simplify the function: Plug in \( x = 5 \) into \( f(x) = 2x + 3 \):
[tex]\[ f(5) = 2(5) + 3 \][/tex]
3. Perform the arithmetic: Calculate \( 2(5) + 3 \):
[tex]\[ f(5) = 10 + 3 = 13 \][/tex]
So, the limit of \( f(x) \) as \( x \) approaches 5 is 13. Therefore,
[tex]\[ \lim _{x \rightarrow 5} f(x) = 13 \][/tex]
This means the function \( f(x) \) approaches the value 13 as \( x \) gets closer and closer to 5.
Additionally, if we revisit our function \( f(x) = 2x + 3 \), we can see that it's a linear function, meaning its limit at any point \( x = a \) is simply the value of the function at that point \( a \). So the limit process is straightforward since the function is continuous and defined for all real values of \( x \).
Therefore, the detailed solution to our limit in question is:
[tex]\[ \lim _{x \rightarrow 5} f(x) = 13 \][/tex]
Here are the steps to solve for the limit:
1. Substitute the value of \( x \): The first step in finding the limit is to directly substitute the value \( x = 5 \) into the function \( f(x) \).
2. Simplify the function: Plug in \( x = 5 \) into \( f(x) = 2x + 3 \):
[tex]\[ f(5) = 2(5) + 3 \][/tex]
3. Perform the arithmetic: Calculate \( 2(5) + 3 \):
[tex]\[ f(5) = 10 + 3 = 13 \][/tex]
So, the limit of \( f(x) \) as \( x \) approaches 5 is 13. Therefore,
[tex]\[ \lim _{x \rightarrow 5} f(x) = 13 \][/tex]
This means the function \( f(x) \) approaches the value 13 as \( x \) gets closer and closer to 5.
Additionally, if we revisit our function \( f(x) = 2x + 3 \), we can see that it's a linear function, meaning its limit at any point \( x = a \) is simply the value of the function at that point \( a \). So the limit process is straightforward since the function is continuous and defined for all real values of \( x \).
Therefore, the detailed solution to our limit in question is:
[tex]\[ \lim _{x \rightarrow 5} f(x) = 13 \][/tex]
