Notation Question: Understanding "y --> 2^(-) implies y < -2

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In summary, the conversation is about understanding the notation for left-hand limits, which is represented as y --> 2^(-). The person asking the question is confused about why it's not y --> -2^(-) and the other person clarifies that it is a mistake in the book. The conversation ends with the person thanking the other for their help in understanding the notation.
  • #1
chemistry1
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Hi,

I have a question about : http://imgur.com/RU7PvtJ

I actually understand what I need to do. I need to see if both one sided limits are the same to establish that the limit exists. The only thing which I just find weird is the "since y --> 2^(-) implies y<-2"

Can somebody explain me where this y --> 2^(-) is coming from ??
 
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  • #2
It is just a notation to denote the left-hand limits. So

[tex]\lim_{x\rightarrow a^-} f(x)[/tex]

is the limit of ##f(x)## as ##x\rightarrow a## but ##x<a##.
 
  • #3
But shouldn't we say : y --> -2^(-) and not y --> 2^(-) ?
 
  • #4
chemistry1 said:
But shouldn't we say : y --> -2^(-) and not y --> 2^(-) ?

Yes, you are correct. The book is wrong there (and it is wrong is the same place on the next line too).
 
  • #5
micromass said:
Yes, you are correct. The book is wrong there (and it is wrong is the same place on the next line too).
Yes, I also noticed it. Ok, thank you!
 

1. What does "y --> 2^(-)" mean?

This notation indicates that y approaches 2 from the negative direction. In other words, y is getting closer and closer to 2 from values that are less than 2.

2. How is this notation different from "y --> 2^(+)"?

When the "^" symbol is followed by a positive sign, it indicates that y approaches 2 from the positive direction. This means that y is getting closer and closer to 2 from values that are greater than 2.

3. What is the significance of the arrow in this notation?

The arrow represents the idea of "approaching." It shows the direction in which y is getting closer to 2.

4. How does "y < -2" relate to the notation "y --> 2^(-)"?

The notation "y --> 2^(-)" implies that y is approaching 2 from values that are less than 2. Since y is getting closer to 2 from values that are less than 2, it follows that y must be less than 2.

5. Can you provide an example of a situation where this notation is useful?

This notation is often used in calculus to represent the limit of a function as it approaches a specific value. For example, if we have the function f(x) = 1/(x-2), we can say that f(x) --> 2^(-) as x approaches 2 from the left side of the number line. This notation is also useful in understanding the behavior of functions near specific values.

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