How to find this limit?

[OmarMohamedKhallaf]

I don't quit understand how should I solve this problem:
[MATH] \lim\limits_{x \to 3} f(x)=\left\{\begin{array}{cc} \left|x-3\right| & \hspace{5mm}, x \ne 3 \\ 2 & \hspace{5mm}, x = 3 \end{array}\right. [/MATH]I know I should find [MATH]\lim\limits_{x \to 3^{+}} \text{ and } \lim\limits_{x \to 3^{-}}[/MATH], but which function I should use for [MATH]\lim\limits_{x \to 3^{+}}[/MATH] and which I should use for [MATH]\lim\limits_{x \to 3^{-}}[/MATH]If the problem was:
[MATH] \lim\limits_{x \to 3} f(x)=\left\{\begin{array}{cc} \left|x-3\right| & \hspace{5mm}, x < 3 \\ 2 & \hspace{5mm}, x > 3 \end{array}\right. [/MATH]Then I will evaluate [MATH]\lim\limits_{x \to 3^{+}}[/MATH] using the constant function , and evaluate [MATH]\lim\limits_{x \to 3^{-}}[/MATH] using [MATH]\left|x-3\right|[/MATH]

 

[Dr.Peterson]

You use [MATH]f[/MATH] for both one-sided limits!

For the left limit, that means [MATH]x-3[/MATH], since on the left, [MATH]x\ne3[/MATH].

For the right limit, that again means [MATH]x-3[/MATH], since on the right, [MATH]x\ne3[/MATH].

 

[Steven G]

It doesn't matter what happens at x=3 when computing the limit

 

[OmarMohamedKhallaf]

Thank you all, I don't know how I missed that.