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

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) (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 as x approaches 3 from the left (below) =
The limit of as x approaches 3 from the right (above) =
As we can see, the two limits are the same. So the limit exists and it is 5:

If the two limits had not been the same then would not exist.

RELATED QUESTIONS
For the piecewise function, find the values g(-7),g(2), and g(4) g(x)= x+4, for x<2 (answered by Edwin McCravy)

For the piecewise function, find the values g(−2),... (answered by jim_thompson5910)

Please help me sketch the graph of this piecewise- defined function.? f(x)= {2x-3 if... (answered by MathLover1)

Evaluate the piecewise function at the given value of the independent variable. (answered by jim_thompson5910)

Let g be the function defined by g(x) = {- 1/2x+3 if x < 5 { {... (answered by Fombitz)

Please help me sketch the graph of this piecewise- defined function? f(x)= {3 if x<1... (answered by ewatrrr)

Find the domain of each function. 1. g(x)=5x+1 2. g(x)=x-7 3. g(x)= /x 4. g(x)=... (answered by Boreal)

Let g be the function defined by g(x) = { -1/2x+3 if x < 5 { { √x-5 if x ≥ (answered by stanbon)

Let g be the function defined by g(x) = { -1/2x+3 if x < 5 { {... (answered by stanbon)