Please answer 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30. Please do it on paper bc it's really hard to understand when is written on here. Also, please show step by step how you got that answer.

Find the limit using the algebraic method. Verify using SYNTHESIS the numerical or graphical method. Find the limit, if it exists. 1. lim (x2 - 3) 2. lim (x2 + 4) * - sin x sin h) sin x cos h - sin x 31. lim h 32. lim h 3. lim ~ 4. lim - x2 + 3x x2 - 2x4 5. lim (2x + 5) 6. lim (5 - 3x) 33. lim - X-ox- 2x4 34. lim - *-0 x2 + 3x X - x2 - 25 x2 - 16 . xVx 7. lim 8. lim 35. lim 36. lim *+ x 2 * - -5 x + 5 x+ 4 xox+ x x-20 xVx - 2 9. lim 10. lim - 2 37. lim x x-2 x2 - x- 2 x+ x- 6 x 2 - - 20 11. lim 12. lim 38. lim x-+ 2 x - 2 x+ 4 x--1 x+1 Find the limit. Use the algebraic method. - 9 13. lim Vx2 - 17 14. lim Vx2 + 5 39. ling 2x - 6 3x2+ 5x - 15. lim (x + sin x) 16. lim (cos x + tan x) 40. lim X -7 /6 *--2 x2 - 3x - 10 I + sin x 1 + cos x 17. lim 18. lim x-+01 - sin x COS X Technology Connection 19. lim x-2x - 2 20. Tim (x - 1)2 Further Use of the TABLE Feature. In Section 2.1, we 3x2 - 4x + 2 21. lim discussed how to use the TABLE feature to find limits. x-"2 7x2 - 5x + 3 Consider 4x2+ 5x - 7 22. lim spar to 20389 sp515v Vi+ x- (--1 3x2 - 2x + 1 x2 + x - 6 23. lim Input-output tables for this function are shown below. * - 2 x 2 - The table on the left uses TblStart = -1 and ATbl = x2 - 16 0.5. By using smaller and smaller step values and begin- 24. lim - x-$4 x2 - x - 12 ning closer to O, we can refine the table and obtain a better estimate of the limit. On the right is an input- 25. lim (6x2 + 6xh + 2h2) output table with TblStart = -0.03 and ATbl = 0.01. 26. lim (10x + 5h) 27. lim -2x - h X h-xox 2 ( x + h ) 2 -1 -0.03 0.503807 -5 -0.5 0.585786 -0.02 0.502525 28. lim h-ox(x+ h) 0 ERROR -0.01 0.501256 O, 0.449490 0 ERROR tan x 29. lim 0.414214 0.01 0.498756 X-0 X 1.5 0.387426 0.02 0.497525 0.366025 0.03 0.496305 30. lim x csc x *-0