设'(x)=dfrac (1)(1+{e)^x}+1,xin (-infty ,+infty )且 '(x)=dfrac (1)(1+{e)^x}+1,xin (-infty ,+infty ) 则 a b 的值为 A a = -1 , b = -2 B a = 1 , b = 2 C a = 1 , b = -2 D a = -1 , b = 2

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

令(x)=lim _(xarrow infty )dfrac (1-{e)^-ax}(1+{e)^-ax},则(x)=lim _(xarrow infty )d

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

(int )_(0)^+infty dfrac (x{e)^-x}({(1+{e)^-x)}^2}dx= ()-|||-__

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

[例3] (int )_(0)^+infty dfrac (x{e)^-x}({(1+{e)^-x)}^2}dx

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

极限lim _(xarrow infty )dfrac (1+{e)^x}(1-{e)^x}的结果是（ ）极限的结果是（）A.1B.-1C.0D.不存在

lim _(xarrow infty )(x)^2(sqrt (dfrac {1+{x)^2}({x)^2}}-1)= __

(4) (int )_(0)^+infty dfrac (dx)((1+x)(1+{x)^2)}