Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly 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]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.