⑩天掌 Teaching Plan on Advanced Mathematics 例7求lm(1+2x)m ff lim(1+2x)ins=lim(1+2x) 2x siny 6ln(1+2x)2 lim e x→ im|61n(1+2x)2x E A0 SInx 般地对于形如(x)"((x)>0,(x)≠1)的函数 (通常称为幂指函数如果 limu(x)=a>0, lim v(a)=b 则imu(x)=a 「返回 Tianjin Polytechnic Moiwendity wTianjin Polytechnic University Teaching Plan on Advanced Mathematics 例7 求 sinx 3 x 0 lim (1+ 2x) → 6 2x ] 1 ln(1 2 x ) sinx x lim [6 x 0 2x 1 ln(1 2x ) sinx x 6 x 0 6 sinx x 2x 1 x 0 sinx 3 x 0 e e lim e lim (1 2x) lim (1 2x) = = = + = +  + →  + →   → → 解 v x b v x u x a u x a v a b u x u x u x = =  =   ( ) ( ) lim ( ) lim ( ) 0,lim ( ) ( ), , ( ) ( ( ) 0, ( ) 1) 则 通常称为幂指函数 如 果 一般地 对于形如 的函数 返回