Estimate the following limits using graphs or tables.
$\underset{h\to 0}{\lim }\frac{\ln (1+h)}{h}$

Verified step by step guidance

1. Recognize that the limit $\underset{h\to 0}{lim}\frac{\ln (1+h)}{h}$ is a standard limit that can be evaluated using the definition of the derivative.
2. Identify that the expression $\frac{\ln (1+h)}{h}$ resembles the difference quotient for the derivative of $\ln (x)$ at $x=1$.
3. Recall that the derivative of $\ln (x)$ is $\frac{1}{x}$. Therefore, at $x=1$, the derivative is $\frac{1}{1}=1$.
4. Conclude that the limit $\underset{h\to 0}{lim}\frac{\ln (1+h)}{h}$ is equal to the derivative of $\ln (x)$ at $x=1$, which is 1.
5. Alternatively, use L'Hôpital's Rule, which applies to limits of the form $\frac{0}{0}$, by differentiating the numerator and the denominator separately and then taking the limit.