Solve lim x→∞ of 1/x

Step-by-step solution

1. As $x$ grows large, $\frac{1}{x}$ shrinks toward $0$.

2. For any $\varepsilon > 0$, choose $N = 1/\varepsilon$, then $x > N \Rightarrow |1/x| < \varepsilon$.

3. Therefore $\lim_{x \to \infty} \frac{1}{x} = 0$.