证明:若对任何正数ε,有 |a-b|lt c, 则 =b.-|||-4.设 neq 0, 证明 |x+dfrac (1)(x)|geqslant 2, 并说明其中等号何时成立.-|||-5.证明:对任何 in R, 有-|||-(1) |x-1|+|x-2|geqslant 1;-|||-并说明等号何时成立.-|||-(2) |x-1|+|x-2|+|x-3|geqslant 2.

[题目]-|||-3.设 ,bin R, 证明:若对任何正数ε有 |a-b|lt c 则 =b.

[题目]设 gt bgt 0 ,证明: dfrac (a-b)(a)lt ln dfrac (a)(b)lt dfrac (a-b)(b)

[题目]设 gt bgt 0, 证明: dfrac (a-b)(a)lt ln dfrac (a)(b)lt dfrac (a-b)(b).

[题目]设 gt bgt 0 ,证明: dfrac (a-b)(a)lt ln dfrac (a)(b)lt dfrac (a-b)(b)

11.设 gt bgt 0, 证明:-|||-dfrac (a-b)(a)lt ln dfrac (a)(b)lt dfrac (a-b)(b)

23设 x<1, 且 neq 0 时,证明: dfrac (1)(x)+dfrac (1)(ln (1-x))lt 1.

(5)设 (x,y)=ln (x+dfrac (y)(2x)) ,则 _(y)(1,0)= () .-|||-(A)1 (B) dfrac (1)(2) (C)

证明:当 gt 0 时,有不等式 arctan x+dfrac (1)(x)gt dfrac (pi )(2)

证明:当 lt xlt dfrac (pi )(2) 时, tan xgt x+dfrac (1)(3)(x)^3.

证明下列不等式:-|||-(4)当 lt xlt dfrac (pi )(2) 时, tan xgt x+dfrac (1)(3)(x)^3 ;