Calculous graphs and limit problem

Question

i need help with problem 48. here is a pic of the problem. please list all work for each answer.

http://imgur.com/Y25K2sX

thanks in advance

Answer 1

• Part a, you are looking for the limit as x approaches 3 from the positive side.  This is what that little + after the 3 means.  So look at the graph from the right, and G(x) approaches 3.
• Part b, same thing, but from the negative side, or left, so G(x) approaches 1
  
• Part c, you only have a limit IF both the negative limit and the positive limit are the same.  In this case, 3 does NOT equal 1, so no limit exists.
• Part d, G(3) is the actual defined value of G(x) at x=3, and G(3)=1.  You know this from the solid dot there.
• For the next few parts, G is continuous everywhere EXCEPT x=3, where you have that gap.  As I said in another of your questions, to be continuous, you have to be able to draw the graph without lifting your pencil.