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October 3rd, 2012, 07:20 AM  #1 
Member Joined: Oct 2012 Posts: 39 Thanks: 0  Below are the graphs of functions f and g...
I don't understand how the limit is 3? Wouldn't it not exist since they aren't connecting? Why is it Does not Exist? Thanks a bunch for preparing for my test!

October 3rd, 2012, 08:43 AM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Below are the graphs of functions f and g...
Notice that the limit, as x approaches 4, of f(x) does not exist. Same goes for g(x). Drawing a picture of f(x) + g(x) could be quite tedious, but the important point is only (near) x = 4. The limit as x>4 from THE LEFT of f is 5. The limit as x>4 from THE LEFT of g is 2. So the limit as x>4 from THE LEFT of f + g is 5 + (2) = 3. Repeat for right hand limits and you'll see the result. 

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