## Calculus (3rd Edition)

The given limit is $f'(1)$ where $f(x)=\sqrt x$.
By definition, the derivative at a point $a$ is $f'(a)=\lim\limits_{h \to 0}\frac{f(a+h)-f(a)}{h}=\lim\limits_{h \to 0}\frac{\sqrt {1+h}-1}{h}$ $\implies f(a+h)=\sqrt {1+h}$ and $f(a)=1$ $\implies a=1$ and $f(x)=\sqrt x$ The given limit is $f'(1)$ where $f(x)=\sqrt x$