Question

find the limits analytically, show all steps

x²–8 1. lim *+2 X-2 2. lim x3 Vx+1-2 x-3 1 3. lim 3+ x 3 x2 - 2x -15 4. lim *+-3 x2 + 4x +3 x0 X (4+ x)-16 5. lim X>0 x² - 4 6. lim 1+2 r -8 x x+sin x 7. lim 10 X sin²x 8. lim :-) x 3 sin(4x) 9. lim *** sin(3x) r? 10. lim 1981-COSI 1 11. lim x → X-1 = 1 12. lim -x-1 1 13. lim 1 x + (x+3)? 14. lim +55-x 15. lim x-5 Il (5-x)² 16. lim 1-2 -1 2(x-2)² (x-3) 17. lim x3 x-3 18. lim xx-2 x-2 19. lim tan x x → 20. lim sec x 21. lim sex 22. lim cotx

Answer 1

38 8 Geven :- 0 lim 272 2 - x-2 = lim 2² (23 We know that 3.13-a-b) 60726455 X-2 x-2 4.6 = lim (x-2) (2²+2x+4) 272 Putting limit (2) ²+2(2) +4 ☆ 4+4+4 = 12 m (2 23 wete knew that 9²62 fate (ab lim 27.-2 273 2-3 = lim 24 -2 Jarl +2) N3 2-3 (Jx+1+2) - lim da ti - (2 X73 (2-3) (JOXET+2) 7 tim X+3 x-3) 14+1 +2) = lim 123 (175) (1X7+2) I 3+1+2 Jut2 271-29 x + 3 / 2+2

3 lim ato 3+2 3 re lim 3-3-X ko 3 (3+2) X = lim .* Kto 3(3+2).X lim ) x=0 3(3+0 - - 3 (37) 3(3+0 9 m 2 4 lim x=2a-15 2²+42 +3 1-3 lim xt-3 (x-6) (x +55 (x+3)(x H) lim x-5 27-3 atl -3-5 3+1 +84 +2 5 lim (4+x) ² 16 We knew that Larb) ² a ²6 tab +0 x = lim 4²+ x² +&x-16 2 +0 lim 16+x²+8x-16 xro

rb 2 lim 22²782 Ho = lim x(x+8 uto 2x o+8= 28 8 X2 o lim xay We know that a ² 6²(ab Cate] 238 933 =(ab (azabt6²) tim x² (22 (x-7)(x+2) (x3 x322274 = lim (x+2) = 드니 x 722ty 4+4+4 12 x+2 x (3)3 2+2 X+2 3 a atsinx lim ato x We knew that lim sina El YO x = lim xtlim sina 20 2 xto x = lim limt ato 1+1 = 12 m 8 x lim SM²x a> o a lim sinx x x x lim xto = tim no NO x sin2x we know that esi lim Sink =1 nto x Opto x2 o.l.om