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

$$\lim_{t\to0}\tan\Big(1-\frac{\sin t}{t}\Big)=0$$
$$A=\lim_{t\to0}\tan\Big(1-\frac{\sin t}{t}\Big)$$ $$A=\tan\Big(1-\lim_{t\to0}\frac{\sin t}{t}\Big)$$ Recall that $\lim_{x\to0}\frac{\sin x}{x}=1$ with $x=t$ here. $$A=\tan(1-1)$$ $$A=\tan0=0$$