Infinite discontinuity question

In summary, the person asking for help has been trying to solve problems themselves, but often struggles and needs help understanding the given solutions. This conversation was in response to a specific problem where the solution showed that f(1) was defined, but the person asking for help thought it was undefined. They were corrected and thanked the person who helped them.
  • #1
1,169
132
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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  • #2
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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  • #3
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!
 
  • #4
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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  • #5
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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Likes MatinSAR

1. What is an infinite discontinuity?

An infinite discontinuity is a type of discontinuity in a function where the limit of the function at a certain point does not exist because it approaches either positive or negative infinity.

2. How can an infinite discontinuity be identified?

An infinite discontinuity can be identified by graphing the function and looking for a vertical asymptote at a certain point. It can also be identified by calculating the limit of the function at that point and seeing if it approaches infinity.

3. What causes an infinite discontinuity?

An infinite discontinuity is caused by a jump or a break in the function at a certain point, where the limit of the function does not exist because it approaches infinity instead of a finite value.

4. Can an infinite discontinuity be removed?

No, an infinite discontinuity cannot be removed. It is a fundamental property of the function at that point and cannot be changed by altering the function or its domain.

5. How does an infinite discontinuity affect the behavior of a function?

An infinite discontinuity can greatly affect the behavior of a function. It can result in the function having a vertical asymptote, which means the function is undefined at that point. It can also cause the function to have different values on either side of the point, making it discontinuous.

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