SOLUTION: need your help with this function : piecewise function: ----------- x^2 – 4 if x < 3 g(x) = ----------- 2x – 1 if x > 3 The limit of the function g as x approaches 3 i

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Question 637084: need your help with this function :
piecewise function:
------------x^2 – 4 if x < 3
g(x) =
------------2x – 1 if x > 3
The limit of the function g as x approaches 3 is as follows:
Thanks in advance
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The limit exists only if g(x) approaches the same number as x approaches 3 from both sides (right/above and left/below). Since g(x) has different formulas for x's that are above 3 and x's that are below 3 we will need to find two limits and then see if they are same number.

Note: Algebra.com's formula-drawing software does not "do" left and right so just use English:
The limit of x%5E4-4 as x approaches 3 from the left (below) = %283%29%5E2-4+=+9-4+=+5
The limit of 2x-1 as x approaches 3 from the right (above) = 2%283%29-1+=+6-1+=+5
As we can see, the two limits are the same. So the limit exists and it is 5:
lim%28x-%3E3%2C+g%28x%29%29+=+5

If the two limits had not been the same then lim%28x-%3E3%2C+g%28x%29%29 would not exist.