Find the set of values of x for which the inequality `In(1+x)>x/(1+x)` is valid.

The comlete set of values of m for which the inequality (x ^(2) -mx-2)/( x ^(2) + mx +4)gt-1 is satisfied aa x in R, is :

The values of 'x' for which the inequality (x+1)/(x-1)^2<1 is satisfied , is

The set of values of x for which the inequality |x-1|+|x+1|lt 4 always holds true, is

Find all values of k for which the inequality, 2x^(2)-4k^(2)x-k^(2)+1gt0 is valid for all real x which do not exceed unity in the absolute value.

The set of values of 'a' for which the inequality x^(2)-(a+2)x-(a+3)<0 is satisfied by atleast one positive real x,

Find the set of value of 'a' for which the equation 2 cos^(-1) x=a +a^(2) (cos^(-1) x)^(-1) posses a solution.

Find the complete set of values of lambda, for which the function f(x)={x+1,x 1 is strictly increasing at x=1

Find the values of p for which the inequality, (2-log_(2)(p/(p+1)))x^(2)+2x(1+log_(2)p/(p+1))-2(1+log_(2)p/(p+1))gt0 is valid for all real x.