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

$1$
Here, $\lim\limits_{x \to 0^{+}} f(x)=\lim\limits_{x \to \dfrac{\pi}{2}^{-}} \dfrac{\cot x}{\csc x}$ This implies that $\lim\limits_{x \to 0^{+}} (\dfrac{cos x/\sin x}{1/\sin x})=\lim\limits_{x \to 0^{+}} \dfrac{\cos x}{\sin x}(\sin x)$ Thus, $\cos (0)=1$