例如利用泰勒公式求极限im e*sinx-x(1+x) x→0 七3 24 +or sinx=x 3! +0(x3)0 lim e*sinx-x(1+x)_ x→0 (1+x+ +o(x3)-x(1+x) lim 2!3 x-→0 3 2!3! +0(x3) 1 lim x→>0 x3 3( ), 2! 3! 1 3 2 3 o x x x e x x  = + + + + ( ) 3! sin 3 3 o x x x = x − + = − +  → 3 0 sin (1 ) lim x e x x x x x 3 3 3 3 2 3 0 ( )) (1 ) 3! ( )) ( 2! 3! (1 lim x o x x x x o x x x x x x + + + +  − + − + → 3 1 ( ) 2! 3! lim 3 3 3 3 0 = − + = → x o x x x x 例如利用泰勒公式求极限 3 0 sin (1 ) lim x e x x x x x − + →