http://i62.tinypic.com/14iol1v.png

I have watched Khanacademy videos on limit but still don't get how to solve this exercise.

Please show me step by step explanation for 2 equations in given exercise, one equation that doesn't include trigonometry and one that does.

Please link me to internet resource where I can learn how to go through this exercise. Or just let me know what concepts am I supposed to learn.

All help is appreciated, thanks.