((1-x)^(3)(x+2)^(4))/((x+9)^(2)(x-8))>=0

Solve the following rational in equalities (i) ((x-1)(x+2))/((x-3)(x+3)) lt 0 (ii) ((1-x)^(3)(x+2)^(4))/((x+9)^(2)(x-8))ge0 (iii) ((x^(2)-3x+1)^(3))/((x-1)(x+2))le0 (iv) (x(2^(x)-3^(x)))/((x^(2)+x+1)(x-1))gt0 (v) ((x-1)(x-2)(x-3))/((x+1)(x+2)(x+3)) le1 (vi) 1 lt (3x^(2)-7x+8)/(x^(2)+1) le2

((2x-1)(x+3)(2-x)(1-x)^(2))/(x^(4)(x+6)(x-9)(2x^(2)+4x+9))<0

((x-4)^(2005)*(x+8)^(2008)(x+1))/(x^(2006)(x-2)^(3)*(x+3)^(5)0(x-6)(x+9)^(2010))<=0

(x-4)^(3)+(x-9)^(3)+(x-8)^(3)=3(x-4)(x-9)(x-8), find the value of x.

lim_(xto0)(x(z^(2)-(z-x)^(2))^(1//3))/([(8 x z -4x^(2))^(1//3)+(8x z)^(1//3)]^(4)) is

lim_(xto0)(x(z^(2)-(z-x)^(2))^(1//3))/([(8 x z -4x^(2))^(1//3)+(8x z)^(1//3)]^(4)) is

The number of values of x for which sin^(-1)(x^(2)-(x^(4))/3+(x^(6))/9………)+cos^(-1)(x^(4)-(x^(8))/3+(x^(12))/9………)=(pi)/2 , where 0le|x|ltsqrt(3) , is

(x+1)(x+2)(x+3)(x^(2)4x+8)(x-2)=0, then x belongs to

Prove that: ((1)/(4))^(-2)-3x8^((2)/(3))x4^(0)+((9)/(16))^(-(1)/(2))=(16)/(3)