Finding limits to a piecewise function (3 pieces)

AI Thread Summary
The discussion focuses on finding the limit of a piecewise function at x=1, where f(x) is defined as -2 for x<1, 3 for x=1, and x-3 for x>1. The limit as x approaches 1 from the left is -2, and from the right is also -2, leading to the conclusion that the limit at x=1 is -2. Participants emphasize the importance of understanding that the limit does not depend on the function's value at that point, which is 3 in this case. Clarifications are made about the concept of limits and the distinction between the limit and the function's value at a specific point. Understanding these concepts is essential for correctly determining the limit's existence.
AllanW
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Homework Statement


f(x)=-2 when x<1
=3 when x=1
=x-3 when x>1
find the limit at 1 from the left and right sides and at 1.

Homework Equations

The Attempt at a Solution


limit for x when approaching 1 from the left is -2
limit for x when approaching 1 from the right is -2
-I'm not sure if the limit at 1 would be -2, or 3
 
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You're correct, but perhaps you should go back and read about what it means for a limit to equal a value. Does it matter what happens to the function at the point you're approaching?
 
axmls said:
You're correct, but perhaps you should go back and read about what it means for a limit to equal a value. Does it matter what happens to the function at the point you're approaching?
All i need to know is what my limit is at x=1 or if the limit even exists.
 
AllanW said:
All i need to know is what my limit is at x=1 or if the limit even exists.
Which you will learn if you follow axmls's suggestion.
axmls said:
perhaps you should go back and read about what it means for a limit to equal a value. Does it matter what happens to the function at the point you're approaching?
The way things work here at PF is that we help you arrive at an answer, but we won't just give it to you.
 
Mark44 said:
Which you will learn if you follow axmls's suggestion.

The way things work here at PF is that we help you arrive at an answer, but we won't just give it to you.
Okay, would i be correct if i said the limit for x at 1 would be -2?
 
AllanW said:
Okay, would i be correct if i said the limit for x at 1 would be -2?
Yes. Do you understand why?
 
Mark44 said:
Yes. Do you understand why?
I believe it because the limits approaching 1 from the left and right side is -2, what i don't understand is if and where the 'f(x)=3 when x=1' comes into play
 
AllanW said:
I believe it because the limits approaching 1 from the left and right side is -2, what i don't understand is if and where the 'f(x)=3 when x=1' comes into play
What does your book have for the definition of the limit of a function at some number?
 

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