Is it generally true that lim(x-infinity) (e(f(x))e(lim(x-infinity) f(x))?

Answer 1

The expression (\lim_{x \to \infty} (e^{f(x)} e^{\lim_{x \to \infty} f(x)})) can be simplified. If (\lim_{x \to \infty} f(x) = L), then (e^{\lim_{x \to \infty} f(x)} = e^L). Thus, the limit can be rewritten as (\lim_{x \to \infty} (e^{f(x)} e^L) = e^L \lim_{x \to \infty} e^{f(x)}). Therefore, the limit depends on the behavior of (f(x)) as (x) approaches infinity.