Question

If $x>0$ and g is bounded function, then $\underset{n\to \infty }{lim}\frac{f\left(x\right)e^{nx}+g\left(x\right)}{e^{nx}+1}$ is

• A. f(x)
• B. g(x)
• C. None of these

Answer 1

The correct option is A f(x)

$\because \underset{n\to \infty }{lim}\frac{f\left(x\right)e^{nx}+g\left(x\right)}{e^{nx}+1}=\underset{n\to \infty }{lim}\frac{f\left(x\right)+\frac{f\left(x\right)}{e^{nx}}}{1+\frac{1}{e^{nx}}}=\frac{f\left(x\right)+0}{1+0}=f\left(x\right)$