Question: If x \> 0 and g is a bounded function, then $\lim _ { n \rightarrow \infty }$ \(\frac{f(x)e^{nx}...

Question

If x > 0 and g is a bounded function, then

$\lim _ { n \rightarrow \infty }$ $\frac{f(x)e^{nx} + g(x)}{e^{nx} + 1}$ is-

Answer 1

Solution

Q g is a bounded function

Ž value of g is finite.

$\lim _ { n \rightarrow \alpha ^ { - } }$ $\frac{e^{nx}\left\lbrack f(x) + \frac{g(x)}{e^{nx}} \right\rbrack}{e^{nx}\lbrack 1 + 1/e^{nx}\}}$ = $\frac{f(x) + \frac{g(x)}{\alpha}}{1 + \frac{1}{\alpha}}$ = f(x)

Question: If x \> 0 and g is a bounded function, then \(\lim _ { n \rightarrow \infty }\) \(\frac{f(x)e^{nx}...

Solution