证明下列不等式:-|||-(1)当 gt 0 时, https:/img.zuoyebang.cc/zyb_3c22d121526970b1ef2b18a375e6d96d.jpg+dfrac (1)(2)xgt sqrt (1+x);-|||-(2)当 gt 0 时, https:/img.zuoyebang.cc/zyb_3c22d121526970b1ef2b18a375e6d96d.jpg+xln (x+sqrt (1+{x)^2})gt sqrt (1+{x)^2} ;-|||-(3)当 lt xlt dfrac (pi )(2) 时, sin x+tan xgt 2x;-|||-(4)当 lt xlt dfrac (pi )(2) 时, tan xgt x+dfrac (1)(3)(x)^3;-|||-(5)当 gt 4 时, ^xgt (x)^2.