QuestionIn Problems 1-32, use a table or a graph to investigate each limit.
1. $\lim _{x \rightarrow 2}\left(x^{2}-4 x+1\right)$
2. $\lim _{x \rightarrow 2} \frac{x^{2}+3}{x+2}$
3. $\lim _{x \rightarrow-1} \frac{2 x}{1+x^{2}}$
4. $\lim _{s \rightarrow 2} s\left(s^{2}-4\right)$
5. $\lim _{x \rightarrow \pi} 3 \cos \frac{x}{4}$
6. $\lim _{t \rightarrow \pi / 9} \sin (3 t)$
7. $\lim _{x \rightarrow \pi / 2} 2 \sec \frac{x}{3}$
8. $\lim _{x \rightarrow \pi / 2} \tan \frac{x-\pi / 2}{2}$
9. $\lim _{x \rightarrow-2} e^{-x^{2} / 2}$
10. $\lim _{x \rightarrow 0} \frac{e^{x}+1}{2 x+3}$
11. $\lim _{x \rightarrow 0} \ln (x+1)$
12. $\lim _{t \rightarrow e} \ln t^{3}$
13. $\lim _{x \rightarrow 3} \frac{x^{2}-16}{x-4}$
14. $\lim _{x \rightarrow 2} \frac{x^{2}-4}{x+2}$
15. $\lim _{x \rightarrow \pi / 2} \sin (2 x)$
16. $\lim _{x \rightarrow \pi / 2} \cos (x-\pi)$
17. $\lim _{x \rightarrow 0} \frac{1}{1+x^{2}}$
18. $\lim _{x \rightarrow 0} \frac{1}{x^{2}-1}$
19. $\lim _{x \rightarrow 0^{+}}\left(1-e^{-x}\right)$
20. $\lim _{x \rightarrow 0^{-}}\left(1+e^{x}\right)$
21. $\lim _{x \rightarrow 4^{-}} \frac{2}{x-4}$
22. $\lim _{x \rightarrow 3^{+}} \frac{1}{x-3}$
23. $\lim _{x \rightarrow 1^{-}} \frac{2}{1-x}$
24. $\lim _{x \rightarrow 2^{+}} \frac{4}{2-x}$
25. $\lim _{x \rightarrow 1^{-}} \frac{1}{1-x^{2}}$
26. $\lim _{x \rightarrow 2^{+}} \frac{2}{x^{2}-4}$
27. $\lim _{x \rightarrow 3} \frac{1}{(x-3)^{2}}$
28. $\lim _{x \rightarrow 0} \frac{1-x^{2}}{x^{2}}$
29. $\lim _{x \rightarrow 0} \frac{\sqrt{x^{2}+9}-3}{x^{2}}$
30. $\lim _{x \rightarrow 0} \frac{\sqrt{x^{2}+4}-2}{x}$
31. $\lim _{x \rightarrow 0} \frac{1-\sqrt{1-x^{2}}}{x^{2}}$
32. $\lim _{x \rightarrow 0} \frac{\sqrt{2-x}-\sqrt{2}}{2 x}$