# Limits of a picewise function?

1. Apr 14, 2012

### shocklightnin

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

We're given a piecewise function

g(x) = {
x if x < 1
3 if x = 1
2-x^2 if 1<x<=2
x-3 if x > 2
]

and were asked: lim x-> 2-

2. Relevant equations

2-x^2 if 1<x<=2
x-3 if x > 2

3. The attempt at a solution

when i drew it out i was getting that the answer is -2 but the workbook says the answer is zero. times have occured where the answers in this workbook have been wrong, so i would just like someone to verify either one. any help is much appreciated, thanks.

2. Apr 14, 2012

### iRaid

2-x^2 if 1<x<=2 Is all you really need to solve this.. As x approaches 2 from the left, the answer is -2. The other limit = -1 anyway so I don't see how they got 1.

EDIT: They may have thought it's (2-x)^2.. That limit as x->2 is 0..

3. Apr 14, 2012

### SammyS

Staff Emeritus
You may have neglected to include the parentheses.

$\displaystyle \lim_{x\to2^-}\left(2-x^2\right)=-2$

$\displaystyle \lim_{x\to2^-}\left((2-x)^2\right)=0$

4. Apr 15, 2012

### shocklightnin

thanks to both! and nope, book def. says '(2-x^2) and not (2-x)^2, must be a printing error either in book or ans. key, but thank you!