Finding limits to a piecewise function (3 pieces)

  • #1
18
0

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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Answers and Replies

  • #2
941
394
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?
 
  • #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?
All i need to know is what my limit is at x=1 or if the limit even exists.
 
  • #4
34,017
5,672
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.
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.
 
  • #5
18
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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?
 
  • #6
34,017
5,672
Okay, would i be correct if i said the limit for x at 1 would be -2?
Yes. Do you understand why?
 
  • #7
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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
 
  • #8
34,017
5,672
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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