a) [tex]\lim_{x \to 1} f(x)[/tex] exists
As the limit of a function at any certain point can exist, but the function itself may be not defined at that point.
For example, if [tex]f(x) =\frac{ (x^3 - 1) }{(x - 1)}[/tex], then [tex]\lim_{x \to 1}\frac{(x^3 - 1)}{ (x - 1)} = 3[/tex],
So, here f(1) is undefined as there is a hole in the graph of the function f(x) at the point (1,3).
Therefore the correct statement about the function cannot be used to conclude that is defined at x = 1 is [tex]\lim_{x \to 1} f(x)[/tex] exists.
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