Límites y equivalentes infinitesimales: ejercicios y técnicas

Apuntes

Prof. Guillermo Moreno 1 Ejercicos LÌmites - LÌmites Notables - InÖnitÈsimos equivalentes Resolver los siguientes lÌmites: 1: lm x!0 e x 1 sin x = 1 2: lm x!0 e x 1 x 3 = 1 3: lm x!0 (x + 1) 5 1 sin x = 5 4: lm x!0 sin 2 x 1 cos x = 2 5: lm x!0 sin 2 x arctan x ln 2 (x + 1) 3 p x + 1 1
= 3 6: lm x!0 1 cos 2 x x = 0 7: lm x!0 1 cos x x 2 = 1 2 8: lm x!0 x sin x 1 cos x = 2 9: lm x!0 tan (3x) x = 3 10: lm x!0 (cos x) 1=x 2 = e 1 2 11: lm x!0 sin x tan x = 1 12: lm x!0 x p 1 cos x = @ 13: lm x!0 x cot (2x) = 1 2 14: lm x!0 tan x sin x x 3 = 1 2 15: lm x!0 sin x (1 + cos x) x cos x = 2 16: lm x!0 (cos (2x)) 3=x 2 = e 6 17: lm x!0 tan 2 x x = 0 18: lm x!0 ln (1 + x) e x 1 = 1 19: lm x!0 ln (1 + sin x) sin x tan x = 1 20: lm x!0 (1 + 2x) 10 1 x 2 + x = 20 21: lm x!0 sin (2x) 2x = 1 22: lm x!0 sin 3x 2
x 2 = 3 23: lm x!0 tan x 3
x 3 = 1 24: lm x!1 tan (x 1) x 1 = 1 25: lm x!0 1 cos (2x) x 2 = 2 26: lm x!0 1 cos ( p x) x = 1 2 27: lm x!0 ln (1 + 2x) 2x = 1 28: lm x!0 ln 1 + x 2
3x 2 = 1 3 29: lm x!0 ln (1 x) x = 1 30: lm x!0 e 2x 1 3x = 2 3 31: lm x!0 e sin x 1 sin x = 1 32: lm x!0 sin (2x) sin (5x) = 0 33: lm x!0 si...