Calculus lim x--->5 f(x), where f(x) = { x+3 if x <> 5, 4 if x = 5?

Question

The question is lim x--->5 f(x), where f(x) = { x+3 if x <> 5, 4 if x = 5

I am a confused on this one. As x approaches 5 f(x) is approaching 8 but when it gets to 5 it is = 4. This is the same from either direction. So does this mean the lim x-->5 f(x) = 4 or does it not exist? I am taking this by correspondence so I do not have a teacher to ask questions. Please explain your answers.

Answer 1

One thing to remember about limits is that we never actually compute the function at the point itself.  We&#039;re only evaluating the function around the point x=5.  Because of this, the value at x=5 doesn&#039;t actually matter.

Removing the point x=5 from consideration, the function x+3 approaches 8 as x-&gt;5, so that&#039;s our limit: 8.