Suppose f(x) = [ 3x^2 - 4 if x=4] Does lim x approaches 4 f(x) exists ? If so find it. If not, explain why not.

Question

Suppose f(x) = [ 3x^2 - 4 if x<4 ]
                         [ 11x          if x >=4]
Does lim x approaches 4 f(x) exists ?
If so find it.
If not, explain why not.

myininaya · Answer

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So to the right of 4 we have the 11x part of the function 

To the left of 4 we have the 3x^2-4 part of the function 

So to find the limit of f to the right of 4, we evaluate 11x at x=4 So to find the limit of f to the left of 4, we evaluate 3x^2-4 at x=4 

If both of these are the same value after you evaluate then the limit exists and then it is whatever you got from the evaluation of those 2 expressions at x=4 

We say the limit does not exist if both of those expressions don't agree when evaluated at 4.