# Finding limits to a piecewise function (3 pieces)

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1. Jan 30, 2016

### AllanW

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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

Last edited by a moderator: Jan 30, 2016
2. Jan 30, 2016

### axmls

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. Jan 30, 2016

### AllanW

All i need to know is what my limit is at x=1 or if the limit even exists.

4. Jan 30, 2016

### Staff: Mentor

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.

5. Jan 30, 2016

### AllanW

Okay, would i be correct if i said the limit for x at 1 would be -2?

6. Jan 30, 2016

### Staff: Mentor

Yes. Do you understand why?

7. Jan 30, 2016

### AllanW

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. Jan 30, 2016

### Staff: Mentor

What does your book have for the definition of the limit of a function at some number?