Please answer item no. (4, 7, 11, 15) only. Show your complete solution in each item. Let me know what solution did you use (I use LHospital rule). I don't know if the limit in item no. 4, 11, 15 do not exist. As I analyze the direction, there are limits in each item that do not exist. If the item do not exist, just write "not exist". You may give your explanation why that limit do not exist. Thank youuuu!

Solve the limits of the following, if they exist. Show your complete solutions. Box your final answer. IT - 2x 1. lim it cosx 2 sin (x - 7) 2. lim (#-x) 3 1 - cos 3x lim *+0 -2x2 4. (ex + e )sin'x lim *+0 2x2 5 sin 5x 5. lim X-0 6. lim sin 3x (vx + 2 + v2) 7. V2 - v1 + cos x lim sin'x In (1 + x) lim X+0 sin x * + sin x - 1 lim X+0 In(1 + x) - X 10. lim - 11. lim (1 - cos 2x) In(1 + x) *+0 x2 (ex - 1) esin x 12. lim - x-0 esin 2x - 4 sin x - 3 13. lim x-2 V2 cos x - 1 - cos x + sin'x 14. lim *+0 In(1 + x2) (extl - e) (1 - cos 2x) 15. lim *+0 x' + sin x