Find all integers `x` for which `(5x-1)<(x+1)^2<(7x-3)dot`

The largets value of non negative integer for which lim_(x->1){(-a x+sin(x-1)+a]1-sqrt(x))/(x+sin(x-1)-1)}^((1-x)/(1-sqrt(x)))=1/4

Find all values of x for which (x^(3) (x - 1))/((x - 2 )) gt 0 .

Find all value of x for which (x^(3)(x-1))/((x-2))gt 0

Verify Mean Value Theorem, if f(x)= x^(3)-5x^(2)-3x in the interval [a,b], where a=1 and b=3. Find all c in (1, 3) for which f'(c )=0 .

Let sqrt(((x+1)(x-3))/((x-2))) . Find all the real values of x for which y takes real values.

Let y=sqrt(((x+1)(x-3))/((x-2))) . Find all the real values of x for which y takes real values.

Let f:R to [1,oo),f(x)=x^(2)-4x+5 . Then find the largest possible intervals for which f^(-1)(x) is defined and find corresponding f^(-1)(x).

Find the set of all x foir which (2x)/((2x^2+5x+2))>1/((x+1))dot

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

Find all real value of a for which the equation x^4 + (a - 1)x^3+ x^2 + (a - 1)x + 1 = 0 possesses at least two distinct positive roots