Question

In a piece-wise function the limit from the left and right approaches infinity but the function is defined for a finite number at the limit. Is it more correct to put the value of the limit as the finite value or infinity?

Answer 1

infinity.
the finite value doesn't necessarily tell you about the limit

Answer 2

for example

\(f(x) = \frac{1}{x^2}, x \neq 0\)
\(a, x = 0\)

f(0) = a, but
\[\lim_{x \rightarrow 0}f(x)=\infty\]