Practicing Success
$\lim\limits_{\alpha \rightarrow \pi / 4} \frac{\sin \alpha-\cos \alpha}{\alpha-\frac{\pi}{4}}=$ |
$\frac{1}{\sqrt{2}}$ 2 $\sqrt{2}$ 1 |
$\sqrt{2}$ |
$\lim\limits_{\alpha \rightarrow \pi / 4} \frac{\sin \alpha-\cos \alpha}{\alpha-\pi / 4}$ Using L'Hopital's Rule so $\lim\limits_{\alpha \rightarrow \pi / 4} \frac{\cos \alpha+\sin \alpha}{1}=\frac{2}{\sqrt{2}}=\sqrt{2}$ Hence (3) is the correct answer. |