En los problemas del 1 al 22, hallar el límite indicado.

1. \[ \lim_{x\to \pi} \frac{\operatorname{sen} x}{x – \pi} \]
2. \[ \lim_{x\to 0} \frac{\operatorname{sen} 2x}{\operatorname{sen} 3x} \]
3. \[ \lim_{x\to 0} \frac{1 – \cos 2x}{4x^2} \]
4. \[ \lim_{x\to \frac{\pi}{4}} [\tan 2x – \sec 2x] \]
5. \[ \lim_{t\to 0} \frac{1 – \cos t}{\operatorname{sen} t} \]
6. \[ \lim_{x\to 0} \frac{\operatorname{sen}^2 \left(\frac{x}{2}\right)}{\operatorname{sen} x} \]
7. \[ \lim_{x\to 1} \frac{\operatorname{sen}^2(x – 1)}{x^2 – 2x + 1} \]
8. \[ \lim_{x\to 0} \frac{x – \operatorname{sen} 2x}{x – \operatorname{sen} 3x} \]
9. \[ \lim_{x\to 0} \frac{\tan x – \operatorname{sen} x}{x^3} \]
10. \[ \lim_{x\to \frac{\pi}{3}} \frac{1 – 2\cos x}{\pi – 3x} \]
11. \[ \lim_{x\to \frac{\pi}{4}} \frac{\cos x – \operatorname{sen} x}{\cos 2x} \]
12. \[ \lim_{x\to 0} \frac{\sqrt{2} – \sqrt{1 + \cos x}}{\operatorname{sen}^2 x} \]
13. \[ \lim_{x\to 1} \frac{\cos \frac{\pi}{2}x}{1 – \sqrt{x}} \]
14. \[ \lim_{x\to 0} \frac{1 – \cos \sqrt{\cos x}}{x^2} \]
15. \[ \lim_{x\to \frac{\pi}{2}} \frac{1 – \operatorname{sen} x}{(x – \frac{\pi}{2})^2} \]
16. \[ \lim_{\theta\to 0} \frac{(1 – \cos \theta)^2}{\tan^5 \theta – \tan^3 \theta} \]
17. \[ \lim_{x\to 0} \frac{\sqrt{1 + \operatorname{sen} x} – \sqrt{1 – \operatorname{sen} x}}{\tan x} \]
18. \[ \lim_{\theta\to a} \frac{\operatorname{sen} \theta – \operatorname{sen} a}{\operatorname{sen} \left(\frac{\theta}{2}\right) – \operatorname{sen} \left(\frac{a}{2}\right)} \]
19. \[ \lim_{x\to 0} \frac{\cos(a + x) – \cos(a – x)}{x} \]
20. \[ \lim_{x\to 0} \frac{\operatorname{sen}(a + x) – \operatorname{sen}(a – x)}{\tan(a + x) – \tan(a – x)} \]
21. \[ \lim_{x\to \frac{\pi}{6}} \frac{2\operatorname{sen}^2 x – 3\operatorname{sen} x + 1}{2\operatorname{sen}^2 x + \operatorname{sen} x – 1} \]
22. \[ \lim_{x\to \frac{\pi}{4}} \frac{2\tan^2 x – \tan x – 1}{2\tan^2 x – 3\tan x + 1} \]