Evaluate the limit at infinity. f(x) = 4[(x + sin x)/(x)]
lim x→∞ f(x)
The limit of sinx as x approaches infinity = does not exist, which leaves me with x/x or ∞/∞ = 1 so 4(1)=4?
Thanks in advance for the help!
$\displaystyle f(x)= 4\frac{x+ sin(x)}{x}= 4(1+ \frac{sin(x)}{x})$
Now, $\displaystyle -1\le sin(x)\le 1$ for all x so as the denominator goes to infinity, $\displaystyle \frac{sin(x)}{x}$ goes to 0.