Question

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

Answer 1

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_(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.