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
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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  • #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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Likes MatinSAR, SammyS and member 731016
  • #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

Related to Infinite discontinuity question

What is an infinite discontinuity?

An infinite discontinuity occurs at a point where a function approaches infinity (positive or negative) as the input approaches the discontinuity point. This means the function's values increase or decrease without bound near that point.

How can you identify an infinite discontinuity on a graph?

An infinite discontinuity is identified on a graph where the function shows a vertical asymptote. As the input value gets closer to the point of discontinuity, the function's value will shoot up to positive or negative infinity, creating a vertical line that the function approaches but never touches.

What causes an infinite discontinuity in a function?

Infinite discontinuities are often caused by division by zero in rational functions. For example, in the function f(x) = 1/(x - a), the function will have an infinite discontinuity at x = a because the denominator becomes zero, causing the function's value to approach infinity.

Can an infinite discontinuity be removed?

No, an infinite discontinuity cannot be removed. Unlike removable discontinuities, which can be fixed by redefining the function at a single point, infinite discontinuities are inherent to the function's behavior as it approaches the discontinuity point.

What is the difference between an infinite discontinuity and a jump discontinuity?

An infinite discontinuity occurs when the function's value approaches infinity as the input approaches the discontinuity point. A jump discontinuity, on the other hand, occurs when the function has a finite but sudden change in value at the discontinuity point. In a jump discontinuity, the left-hand and right-hand limits exist but are not equal.

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