第二章极限论 tan x-sin x tan x-sn x=lim (1-cos x) x→0 tan x-sin (x+o(x))-(x+o(x))o(x) (x+o(x)+o(x2) lim sin x(1-cosx =lim =m(2 +x(x)+o(x)x+(x) +o(x3)+o(x3)+o(x2) =lim 关于无穷小的运算: (1)当p≥k,则o(x4)+o(x)=o(x2) (2)当A为非零常数时,o(Ax)=0(x2) (3)o(x2)o(x)=o(x4+) (4)当P>k,则o(x”)/x4=o(x-) 第二章极限论第二章 极限论 第二章 极限论 解： 3 0 tan sin lim x x x x − → = 3 0 lim x x x x − → =0 3 0 tan sin lim x x x x − → = ( ) 3 0 sin 1 cos lim x x x x − → = 3 2 0 2 lim x x x x→ = 2 1 3 0 tan sin lim x x x x − → = ( ) ( ) 3 0 ( ) ( ) lim x x o x x o x x + − + → = 3 0 ( ) lim x o x x→ =       → 2 0 ( ) 1 lim x x o x x ( ) 3 0 sin 1 cos lim x x x x − → = ( ) 3 2 2 0 ( ) 2 ( ) lim x o x x x o x x         + + → = ( ) 3 2 2 2 2 3 0 ( ) 2 ( ) ( ) 2 lim x o x x x o x o x x x         +  + + → = 3 3 3 4 3 0 ( ) ( ) ( ) 2 lim x o x o x o x x x         + + + → = 2 2 1 lim 3 3 0 =         → x x x 关于无穷小的运算: (1) 当 p  k , 则 ( ) ( ) ( ) k p k o x + o x = o x (2) 当 A 为非零常数时， ( ) ( ) k k o A x = o x (3) ( ) ( ) ( ) k p k p o x o x o x +  = (4) 当 p  k , 则 ( ) ( ) p k p k o x x o x − =