证明不等式：ln(1+e^x)-x＞(1)/(e^x)+1，xin (-infty ,+infty ).

设(x)=dfrac (1)(1+{e)^x}+1,xin (-infty ,+infty )且 (x)=dfrac (1)(1+{e)^x}+1,xin (-

证明等式 arctan x=arcsin dfrac (x)(sqrt {1+{x)^2}} , in (-infty ,+infty

用拉格朗日中值定理证明不等式：(x)/(1+x)＜ln（1+x）＜x（x＞0）．用拉格朗日中值定理证明不等式：$\frac{x}{1+x}$＜ln（1+x）＜x

例25、当 gt 1 时,证明不等式 ln xgt x-1 -

求lim _(xarrow infty )dfrac (ln (x+sqrt {{x)^2+1)}-ln (x+sqrt ({x)^2-1})}({({e)^d

2、设f(x)=(x-1)(2x+1),xin(-infty,+infty)，则在((1)/(2),1)内曲线f(x)（ ）A. 单调增凹的；B. 单调减凹的

((1+dfrac {1)(x))}^(x^2)-|||-.-|||-.arrow +infty e .x

(int )_(-infty )^infty (e)^xg(x+1)dx=_________._________.

lim _(xarrow +infty )((1+{e)^x)}^dfrac (1{x)};

lim_(x to +infty) ((1+frac(1)/(x))^x^2)(e^x) $\lim_{x \to +\infty} \frac{\left(1