`3(1-x) lt 2(x+4)`

3x-2 lt 2x+1

Solve log_(3)(x+2)(x+4)+log_(1//3)(x+2) lt 1/2 log_(sqrt3)7 .

If x gt 0 , prove that, x-x^(2)/2 lt log (1+x) lt x-x^(2)/(2(1+x))

Solve (1/2)^(x^(6)-2x^(4)) lt 2^((x)^(2)) .

Integrate : int "tan"^(-1)(2x)/(1-x^(2))dx(-1 lt x lt 1)

A bag contains 50 tickets 1,2,3,...50 of which 5 are drawn at random and aranged in ascending order of their numbers x_(1) lt x_(2) lt x_(3) lt x_(4) lt x_(5) . Find the number of selections so that x_(3)=30

The set of all values of x for which ((x+1)(x-3)^(2)(x-5)(x-4)^(3)(x-2))/(x) lt 0

Let f(x)={(x^(2)-4x+3",",x lt 3),(x-4",",x ge 3):} and g(x)={(x-3",",x lt 4),(x^(2)+2x+2",",x ge 4):} . Describe the function f//g and find its domain.

Let f(x)={(x^(2)-4x+3",",x lt 3),(x-4",", x ge 3):} and g(x)={(x-3",",x lt 4),(x^(2)+2x+2",",x ge 4):} Then which of the following is/are true?