!"#!$#%&' (')#*+)$,' -!$.#%/$0'0 0# 12$3# Ingeniería Matemática FACULTAD DE CIENCIAS FÍSICAS Y MATEMÁTICAS UNIVERSIDAD DE CHILE Introducción al Cálculo 08-1 45&' 6+/$,' !"!#$%&'# (' )!#'*%+'+ +! (', ,%-.%!&"!, '/#$'*%0&!,1 78 lı́m x = 02 x→0 98 :8 ;8 <8 =8 lı́m x = 02 x→0+ 1 x lı́m 1 ln(x) lı́m 1 | ln(x)| lı́m 1 − x→0+ x→0+ 1 lı́m e x x→0− >8 lı́m x→0− ?8 = 02 x→1 &0 !3%,"!2 = +∞2 &0 !3%,"!2 √ −x &0 !3%,"!2 4'#' "0+' 5.&*%6& f ,% x→x lı́m lı́m 2f (x) = 2 + u2 x→x f (x) = u 0 0 @8 7A8 1 lı́m 2 x→0+ ln(x ) = 22 lı́m ln(x2 ) = +∞2 x→0 778 lı́m ex = 02 x→0 798 lı́m ln(x) = 12 x→1 7:8 lı́m sen(x) = 02 x→0 7;8 lı́m e · ex = 02 x→−1 lı́m ln( xe ) = 02 7<8 x→e 7=8 x→π lı́m sen(π − x) = 12 789 !&"0&*!, !"#!$#%&' (')#*+)$,' -!$.#%/$0'0 0# 12$3# 456 476 lı́m xex = 0 x→+∞ lı́m ax = 0 x→0 486 1 lı́m x x = 0 x→0 9:6 lı́m xx = 1 x→0 946 996 lı́m sen(x) = +∞ x→+∞ lı́m tan(x) = 1 x→0 9;6 9<6 x→0 ex −e−x 2 lı́m √ x=0 lı́m =1 x→0 9=6 lı́m √ x=2 x→1 9>6 lı́m log2 (x) = 3 x→8 956 976 lı́m ln(x) = 1 x→e lı́m exp(x) = −e4 x→−4 986 ;:6 lı́m 3+4x2 x→−4 6−x !" #$%&'# lı́m log3 (x) + √ x=5 x→9 ;46 x→π ;96 x→+∞ ;;6 x→+∞ ;<6 ;=6 lı́m cos(x) + sen(x) = −1 lı́m x + ln(x) = 0 lı́m x2 + ln(x) = +∞ lı́m (1 + x2 ) · ln(x) = −∞ x→0+ lı́m x→0 ;>6 ;56 sen(x) x =0 lı́m ex −1 x lı́m ln(1+x) x x→0+ =1 !" #$%&'# x→0− ()*