`(|x+1|-x)/x<1`

Differentiate the following w.r.t. x : (x + 1/x)^x + x^(x + 1/x)

Evaluate: ("Lim")_(x->1)(x^x-x)/(x-1-lnx)

If f(x)=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)):}| then

If |(1+x,1-x,1-x),(1-x,1+x,1-x),(1-x,1-x,1+x)|=0 then x=

If f(x) = |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x-1))| , using properties of determinant, find f(2x) - f(x).

Solve that |{:(1+x,1-x,1-x),(1-x,1+x,1-x),(1-x,1-x,1+x):}|=0

If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f(500) is equal to a. 0 b. 1 c. 500 d. -500

If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f(500) is equal to a. 0 b. 1 c. 500 d. -500