Infinite discontinuity question

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Homework Help Overview

The discussion revolves around the concept of infinite discontinuity in relation to a specific function, particularly focusing on the continuity of the function at the point where a vertical asymptote may exist.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the definition of continuity and the implications of a vertical asymptote on the function's continuity at a specific point. There are attempts to clarify whether the function is defined at that point and how that affects continuity.

Discussion Status

Some participants are exploring different interpretations of the function's behavior at the point of interest, with one participant asserting that the function is defined at that point, while another questions this assertion. There is a mix of agreement and differing views on the continuity of the function.

Contextual Notes

Participants express uncertainty regarding the definitions and implications of continuity and discontinuity, particularly in the context of vertical asymptotes. There is mention of a graph that is referenced but not provided in the discussion.

member 731016
Homework Statement
Please see below
Relevant Equations
Please see below
For 6(b),
1676575875785.png

The solution is,
1676575903178.png


However, for ##a = 1## they could have also said that f is not continuous since f(1) is not defined (vertical asymptote) correct?

Many thanks!
 
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Callumnc1 said:
Homework Statement:: Please see below
Relevant Equations:: Please see below

For 6(b),
View attachment 322376
The solution is,
View attachment 322377

However, for ##a = 1## they could have also said that f is not continuous since f(1) is not defined (vertical asymptote) correct?

Many thanks!
No.

The graph for problem 6. clearly shows that f(1) is defined. It appears to have the same value as f(3).
 
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SammyS said:
No.

The graph for problem 6. clearly shows that f(1) is defined. It appears to have the same value as f(3).
Oh true! Thank you for you for help @SammyS!
 
Callumnc1 said:
Homework Statement:: Please see below
Relevant Equations:: Please see below

For 6(b),
View attachment 322376
The solution is,
View attachment 322377

However, for ##a = 1## they could have also said that f is not continuous since f(1) is not defined (vertical asymptote) correct?

Many thanks!
Do you attempt to do these problems yourself, or do you just look at the solutions? Usually, it seems, you also need help following the given solutions.
 
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PeroK said:
Do you attempt to do these problems yourself, or do you just look at the solutions? Usually, it seems, you also need help following the given solutions.
Thank you for your reply @PeroK!

I often attempt the problems myself, but I get it wrong and sometimes don't understand the solutions.

Many thanks!
 
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