#### Answer

$$ \lim_{x\to \infty} f(x) \approx 0.135$$

#### Work Step by Step

(a) Given $$f(x) =\left(1-\frac{2}{x}\right)^x $$
From the figure , it is clear that as $x\to\infty$ $f(x)\to 0.135$
(b) by using values of $x$ , we get
$ f(10)=0.107374$, $f(100) =0.135064$, $f(1000) =0.1353327$, and $f(10000) =0.1353352$ , then
$$ \lim_{x\to \infty} f(x) \approx 0.135$$