Prove the following inequality:
`e^(x) gt x+1 " "" for"" " x in (0,oo)`

Solve the following inequation: 1/(x-2)<0

Solve the inequality Q(x)=x^(3)-4x^(2)+4x gt0 .

Solve the inequation: - 1/(x+2)gt0

The inequality x^(2)-3x gt tan^(-1) x is ture in

Solve the following inequalities: (x^(2)-3x-18)/(13x-x^(2)-42)gt0

Prove the following : e^(-(1)/(e)) lt int_(0)^(1)x^(x)dx lt 1

Solve the system of inequation: x+3gt0, 2xlt14

The ordered pairs (3,-1) satisfies which of the following inequalities? I. x+3y gt0 II. 2x+3y gt2 III. x+y lt 0

Let I_(1) : (log_(x)2) (log_(2x)2) (log_(2)4x)gt1 I_(2) : x^((log_(10)x)^(2)-3(log_(10)x)+1) gt 1000 and solution of inequality I_(1) is ((1)/(a^(sqrt(a))),(1)/(b))cup(c, a^(sqrt(a))) and solution of inequality I_(2) is (d, oo) then answer the following Both root of equation dx^(2) - bx + k = 0, (k in R) are positive then k can not be