In the following graph, how do you determine the value of c such that #lim_(x->c) f(x)# exists?

enter image source here

1 Answer
May 13, 2018

show below

Explanation:

show below:

For the function in the graph below f(x) is defined when x = -2 but the value which f(x) will approach as x gets closer to -3 from the left is different from the value that it will approach as x gets closer to -3 from the right.
Looking at the graph we can see that as x approaches -3 from the left f(x) approaches (negative two) however as x approaches -3 from the right f(x) approaches (negative three).

enter image source here
so
#lim_(xrarr-3^+)=-3#

#lim_(xrarr-3^-)=-2#

the limit does not exist at #x=-3#

in the same way when x rarr to zero

#lim_(xrarr0^+)=1#

#lim_(xrarr0^-)=+oo#

the limit does not exist at #x=0#

so the values of c equals #c=-3# or #c=0# but the limit doesnot exist.