Answer
$f(x)$ appears to have a limit as $x\to1$, which is $0.367879...$
Work Step by Step
$$f(x)=x^{1/(1-x)}$$
(a) The table is shown below.
As we can see from 2 tables below, as $x$ gets more decimals and approaches $1$, the value of $f(x)$ also gets more decimals and apparently approaches a value of $0.367879...$ from both sides.
Even though, we cannot get an exact value of this number, f(x) still approaches this same value either from the left or the right side as $x\to1$, meaning $f(x)$ appears to have a limit here, which is $0.367879...$
(b) The graph is shown below.
Looking at the graph, we confirm that the closer $x$ approaches $1$, the closer $f(x)$ gets to $0.367879...$.
