Solve Limit: Find \lim_{n\rightarrow +2} {f(x)}

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Homework Help Overview

The discussion revolves around evaluating the limit of a function as it approaches a specific value, specifically focusing on the expression \(\lim_{x\rightarrow +2} {\frac{f(x)-5}{x-2}}=5\) and its implications for finding \(\lim_{n\rightarrow +2} {f(x)}\). The subject area is calculus, particularly limits and continuity.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the relationship between the limit of a ratio and the behavior of its numerator and denominator as they approach zero. There is a discussion about the implications of having multiple functions that can satisfy the given limit condition.

Discussion Status

The conversation is active, with participants questioning the assumptions made about the function \(f(x)\) and discussing the conditions under which the limit exists. Some guidance has been offered regarding the behavior of the numerator in relation to the denominator.

Contextual Notes

There is confusion regarding the variables used in the limit, specifically between \(n\) and \(x\). Participants are also considering the implications of having an infinite number of functions that could satisfy the limit condition, which raises questions about the uniqueness of the function \(f\).

maxitis
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I have the limit:
<br /> \lim_{x\rightarrow +2} {\frac{f(x)-5}{x-2}}=5<br />
And i want to find the:
<br /> \lim_{n\rightarrow +2} {f(x)}<br />
Can i say that f(x)-5=5*(x-2)
And then find the limit?
Thank you
 
Last edited:
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There is some confusion between n and x. Fix that. Then observe that as x (or n) goes to 2, the denominator goes to zero.
 
And why is that a problem?
Both parts will be equal to 0.
 
Because that would prevent you from using the formula you wanted.

But think about it. You have a finite limit of a ratio, whose denominator goes to zero. What can be said about the limit of its numerator in this case?
 
Yes, the denominator goes to 0. So what must the numerator go to in order that a limit exist?
 
maxitis said:
I have the limit:
<br /> \lim_{x\rightarrow +2} {\frac{f(x)-5}{x-2}}=5<br />
And i want to find the:
<br /> \lim_{n\rightarrow +2} {f(x)}<br />
Can i say that f(x)-5=5*(x-2)
And then find the limit?
Thank you
No, because there are, in fact, an infinite number of possible functions, f. f(x)= 5(x- 2)+5 is just one of them.

Yes, the denominator goes to 0. So what must the numerator go to in order that a limit exist?
 
The numerator should be zero.
So we have: f(2)-5=0 Am i right?

Something about before,
Why you said that there are infinite number of functions f that can satisfy that limit?
One is f(x)=5(x-1), can you give me another example?
Thank you
 
Last edited:

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