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LISTA 7

Calcule los limites.( en algunos se ha puesto el resultado) 2 +2x+5 1. l´ x→1 x x2 +1 = 4 ım x−2 2. l´ x→2 √2+x = 0 ım 1 1 3. l´ x→+∞ (2 − x + x2 ) = 2 ım 3 −2x2 4. l´ x→+∞4x 3x3 −5+1 = 4/3 ım 5. l´ x→+∞ x+1 = 1 ım x 6. l´ n→+∞ 1+2+3+···+n = 1/2 ım n2 2 +x+1 7. l´ x→−∞ x 2x+5 = ∞ ım 2 8. l´ x→−∞ 3x x−2x−1 = 0 ım 3 +4 x3 −1 9. l´ x→1 x−1 = 3 ım 2 +2x+5 10.l´ x→1 x x2 +1 = 4 ım 2 −5x+6 11. l´ x→2 xx−12x+20 = 1/8 ım 2 3 2 12. l´ u→−2 u +4u +4u = 0 ım (u+2)(u−3) 13. l´ y→−2 ım 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.
y3 +3y 2 +2y = −2/5 y 2 −y−6 (x−h)3 −x3 = 3x2 l´ h→0 ım h 1 3 l´ x→2 [ x − 1−x ] = −1 ım n −1 l´ x→1 xx−1 = n ım √ l´ x→0 √1+x−1 = 1/2 ım x √ √ 2x+1−3 = 2 2/3 l´ x→4 x−2−√2 ım √ x2 +p2−p l´ x→0 √ 2 2 = q/p ım x +q −q √ 1+x+x2 −1 √ l´ x→0 ım = 1/2 √ x 2 −3 l´ x→+∞ √x 3 +1 = 1 ım 3 √x x2 +1 l´ x→−∞ x+1 = −1 ım √ √ l´ x→+∞ ( √2 + 1 − x2 − 1) = ım x l´ x→+∞ x(√x2 + 1 − x) =1/2 ım l´ x→−∞ x( x2 + 1 − x) = −∞ ım 1 − 1 l´ x→+∞ x −x2 = ım 1 1 (w3 +2w)4 1 l´ w→−∞ [ w5 +w4 −w2 ] 3 = ım l´ x→−∞ (−x7 − 2x4 + 3) ım
x3 x4

0

= 1

29. l´ x→0 g(x), donde ımg(x) = 30. l´ t→−2 f (t) donde ım t + 4 if t < −2 if t = −2 f (t) = 0  2  t if t > 2 31. l´ x→2 (3 + |2x − 4|) ım 32. Sea 
    

x − 2 if x < 0 x3 − 3 if x > 0

−2 if x <−π f (x) =  sin(x − π/6) if −π < x < π  −2 if x ≥ π

calcula l´ x→−π− f (x), l´ x→−π+ f (x), l´ x→−π f (x). ¿Cuanto vale l´ x→π f (x)? ım ım ım ım 33. l´ x→0 (x|x| + 1) ım 34. l´ x→0sin 3x ım sin 5x 35. l´ x→0 1−cos x ım x2 sin(a+x)−sin(a−x) 36. l´ x→0 ım = 2 cos a x tan x−sin x 37. l´ x→0 ım x3 sin 38. l´ x→0 √ x ım tan x √ 39. l´ x→0 1+sin x− 1−sin x ım x 40. l´x→π/4 sin x−cos x ım 1−tan x 41.l´ x→π/3 1−2 cos x ım π−3x 42. l´ x→π 1−sin(x/2) ım π−sin x 43. l´ x→−2 tan πx ım x+2
√

44. l´ x→+∞ ım

√ x2 −2x+6− x2 +2x−6 2 −4x+3 x

2...