# Limit values?

• Aug 30th 2010, 06:25 PM
GOPgabe
Limit values?
I was given a calculus assignment, and don't quite get what the teacher meant. Any aid is appreciated.

f(x){X^2 X less than or equal to 2
8-2x for 2 < X< 4
4 for X> or equal to 4}

Identify the values of c for which the lim x approaches c of f(x) exist.

What is c, what does this mean?
• Aug 30th 2010, 08:44 PM
Quote:

Originally Posted by GOPgabe
I was given a calculus assignment, and don't quite get what the teacher meant. Any aid is appreciated.

f(x){X^2 X less than or equal to 2
8-2x for 2 < X< 4
4 for X> or equal to 4}

Identify the values of c for which the lim x approaches c of f(x) exist.

What is c, what does this mean?

You are supposed to find the point c where the graph is continuous. One way is to sketch the graph and you will see that the graph is continuous at x=2. To prove it,

take limits as x approaches 2^- and 2^+, and also calculate f(2).

If $\lim_{x\rightarrow 2^-}=\lim_{x\rightarrow 2^+}=f(2)$

Then the graph is continuous at x=2.