SOLUTION: f(x)={x+2 if x<-2 f(x)={2 if x>-2 Find the following limits, if they exist. 1. limx&#8594;&#8722;2&#8722;f(x)limx&#8594;&#8722;2&#8722;f(x) = 2. limx&#8594;&#8722;2+f(x)

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Question 1097659: f(x)={x+2 if x<-2
f(x)={2 if x>-2
Find the following limits, if they exist.
1. limx→−2−f(x)limx→−2−f(x) =
2. limx→−2+f(x)limx→−2+f(x) =
3. limx→−2f(x)limx→−2f(x) =

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!



This is the graph:



Notice that f(x) has no value at x = -2.

1. 

This asks "What is the y-value of the point the graph is
approaching from the LEFT as x gets closer and closer to where x
is -2?"  Although the graph does not get to the point (-2,0), it
nevertheless does APPROACH that point from the LEFT side.  Since
the y-coordinate of the point that the curve approaches from the
left is 0, that is the limit from the left.  Remember it only
APPROACHES the point (-2,0), so it only APPROACHES its limit.
it does not have to "get there" in order to approach it. So



2. 

This asks "What is the y-value of the point the graph is
approaching from the RIGHT as x gets closer and closer to where x
is 2?"  Although the graph does not get to the point (-2,2), it
nevertheless does APPROACH that point from the RIGHT side.  Since
the y-coordinate of the point that the curve approaches from the
left is 2, that is the limit from the RIGHT.  Remember it only
APPROACHES the point (-2,2), so it only APPROACHES its limit.
it does not have to "get there" in order to approach it. So



3. 

Notice that there is no + or - above the -2.  That asks what is the 
y-coordinate of the ONE point that the graph approaches whether 
from the left or right?  Since there is no ONE value that the 
graph approaches from BOTH sides, because the answers to part
1 and part 2 are different, this is undefined, so



Edwin
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