Limit to infinity

The graph of $y = \frac{1}{x}$ has a horizontal asymptote of $y = 0$ meaning that as $x$ increases, the value of $y$ tends to 0.

Another solution would be to say that $\dfrac{\text{constant}}{\infty} = 0.$

set $\infty=99999$

$\large \displaystyle \lim_{x \to \infty} \frac{1}{x}=\frac{1}{99999}=0.00001\approx 0$

Limit means approach.When the numerator is a constant and the denominator get bigger then by the rules of fractions it get smaller.

So $\displaystyle \lim_{x \to \infty} \frac{1}{x}=\boxed{\large{0}}$

$\frac {1}{9} ≈ 0.1111, \frac {1}{99} ≈ 0.0101, \frac {1}{999} ≈ 0.001,$ and so on. As the denominator approaches $\infty$ , $\frac{1}{x}$ gets closer to $\boxed{0}$ .