lim_(n to infty ) ( frac ( 4 ) ( pi ) arctan frac ( n ) ( n + 1 ) ) ^ ( n ) = ( ) . (A.) e ^ ( - frac { 2 ) ( pi ) } (B.) e ^ ( - frac { pi ) ( 2 ) } (C.) frac ( pi ) ( 2 ) (D.) frac ( 2 ) ( pi )

40.求极限lim_(ntoinfty)((n+1)/(1^2)+n^(2)+(n+frac(1)/(2))(2^2+n^2)+...+(n+frac(1)/(

已知 $f(x) = \lim_{n \to \infty} \frac{\ln(e^n + x^n)}{n}$, $(x > 0)$.(1) 求 $f(x)$

求极限$\lim _{n \infty}\left(\frac{1}{n^{2}+n+1}+\frac{2}{n^{2}+n+2}+\cdots+\frac{n

18 单选 lim_(n to infty) ((n)/(n+1))^n=( ).A. eB. 1C. 1/eD. ∞

类似地，设f(x)在x=a处可导，且f(a)≠0，则lim_(n to infty ) [ ( n int _(a)^a+frac (1)/(n) f(x)d

注 类似地，设f(x)在x=a处可导，且f(a)≠0，则lim_(n to infty ) [ ( n int _(a)^a+ frac (1)/(n) f(

设 A_n = (0, (1)/(n))，n in N，则 lim_(n to infty) A_n = ( )A. $(0, 1)$B. $(0, \frac

根据数列极限的定义证明：(1) lim_(n to infty) (1)/(n^2) = 0;(2) lim_(n to infty) (3n+1)/(2n+1

__-|||-lim _(narrow infty )([ sin (dfrac {pi )(4)+dfrac (1)(n))] }^n=( )A.

12 lim_(n to infty) (1+2+3+...+(n-1))/(n^2);12 $\lim_{n \to \infty} \frac{1+2+3+