## University Calculus: Early Transcendentals (3rd Edition)

$9$
Here, we have $\dfrac{dc}{dx}=\dfrac{1}{2 \sqrt x}$ $\dfrac{dc}{dx}=(1/2)x^{-1/2}$ This implies that $c=\int_0^{x} \dfrac{1}{2} t dt$ or, $[t^{1/2}]_0^{x}=\sqrt x$ Thus, $c(100)-c(1)=\sqrt {100}-\sqrt 1=10-1=9$