Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
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]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.