Giíi h¹n_Qu¸ch Duy TuÊn 1) 1 352 lim 23 23 1 −+− +− → xxx xx x → -2 2) 32 38 lim 2 1 −+ −+ → xx x x →1/24 3) 2 24 lim 3 2 − − → x x x → 1/3 4) 1 75 lim 2 3 23 1 − +−− → x xx x → -11/24 5)[§HQG_A97] x xx x 3 0 812 lim −−+ → → 13/12 6)[§HSPHN_B00] 1 57 lim 2 3 1 − −−+ → x xx x → 7/12 7*)[§HTL_01] 2 3 0 3121 lim x xx x +−+ → → 1/2 (Thªm bít 1 + x) 8) x ax n x 11 lim 0 −+ → (a ≠ 0) → a/n (§Æt t = n ax + 1 ) 9) x xx x 5 1312 lim 53 0 +−+ → → 1/75 10)[§HSPHNII_A99] 1 212 lim 5 4 1 − −+− → x xx x →7/10 11)[§HQG_A98] 1 23 lim 3 1 − −− → x xx x → 3/2 12) x x x 2 3sin lim 0 → → 3/2 13) xtg x x 4 3sin lim 0 → → 1/2 14) x xtgx x 5 23sin lim 0 + → → 1 15) 2 0 2coscos1 lim x xx x − → → 5/2 16) 2 0 2coscos4cos lim x xxx x − → → -11/2 17) x ee bxax x − → 0 lim → a – b 18) [HVKTQS_97] 2 0 sin lim x xtgx x − → → 1/2 19*)[§H TN_A97] 2 sin cos 2 cos lim 2 0 x x x       → π → π 20)[§HSP Vinh_B99] xx xx x 2cos2sin1 2cos2sin1 lim 0 −+ −− → → -1 21) x xx x sin 243 lim 0 −−+ → → -1/4 22*)[§HAN_00] x xxx x 7sin 7cos5cos3cos1 lim 2 0 − → → 1 23) 3 23 2 12 1 lim +++ ++ −∞→ xxx xx x → -1/ 3 2 24) )1(lim 2 xxx x +++ −∞→ → -1/2 25)[§HGT_95] 1 21 lim 3 1 − −+ → x x x →3/2 2 , 3 x =t 26)[HVNH_98] 1 12 lim 1 − −− → x xx x → 1/2 27)[§H§N_AB99] 1 132 lim 2 1 − +− → x xx x → 5/8 28)[§HH§_D01] 1 533 lim 3 2 1 − +−+ → x xx x → -1/4 29)[§HSPV_01] x xxx x 3 3 3 2 0 11 lim +−++ → → 1/3 30)[§HHH_98] xx x xtg sin 1 2 0 )1(lim + → → e 31)[§HHH_99] x ee xx x sin lim sin2sin 0 − → → 1 32)[§HTM_99] 2 2 0 cos1 lim x xx x −+ → → 1 33)[§HQGHN_D00] x xx x sin 112 lim 3 2 0 +−+ → → 1 34)[§HSPHN_D00] )1sin( 2 lim 3 1 + ++ −→ x xx x → 4 35)[§H§§_AV00] xx xx x +−− +−− → 11 11 lim 2 0 → 1/2 36)[C§SPMGTW1_01] nx xtg nx + −→ π lim → π, x+n=t 37)[§H§§_BD00] x x x 11sin 7cos1 lim 2 0 − → → 49/242 38)[§H§§_A00] x xx x 11sin 7cos5cos1 lim 2 0 − → → 37/121 39)[§HSP2_A00] a) ) 4 (.2lim 4 xtgxtg x − → π π → 1/2 b) 2 0 cos3 lim 2 x x x x − → → 1/2+ln3 ( Thªm h»ng sè 1, sau ®ã ®Æt t x =− 13 2 ) 40)[§HHH_01] 11 1sincos lim 2 44 0 −+ −− → x xx x → - 4 41)[C§SPHN_D00] x xx x 2 3 0 sin coscos lim − → Giíi h¹n_Qu¸ch Duy TuÊn → -1/12 42)[§HQGHN_A95] 2 2 0 4sinsin2sin lim x xxx x − → → 0 43)[§HGT_97] x x x 1 coslim 0 → → 0 ( Sö dông giíi h¹n kÑp - x x xx ≤≤ 1 cos ) 44)[BCVT_99] xx xx x sin sin lim + − ∞→ → 1 ( Chia c¶ tö vµ mÉu cho x, 0 sin lim = ∞→ x x x ) . 2cos2sin1 2cos2sin1 lim 0 −+ −− → → -1 21) x xx x sin 243 lim 0 −−+ → → -1/4 22*)[ HAN_ 00] x xxx x 7sin 7cos5cos3cos1 lim 2 0 − → → 1 23) 3 23 2 12 1 lim +++ ++