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

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).

so
${\lim}_{x \rightarrow - {3}^{+}} = - 3$

${\lim}_{x \rightarrow - {3}^{-}} = - 2$

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

in the same way when x rarr to zero

${\lim}_{x \rightarrow {0}^{+}} = 1$

${\lim}_{x \rightarrow {0}^{-}} = + \infty$

the limit does not exist at $x = 0$

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