" 178."|x^(3)-1|>=1-x

((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-x^(1/2)))=

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^(2))) where |x|<(1)/(sqrt(3))* Then a value of y is : (1)(3x-x^(3))/(1-3x^(2))(2)(3x+x^(3))/(1-3x^(2))(3)(3x-x^(3))/(1+3x^(2))(4)(3x+x^(3))/(1+3x^(2))

Let f(x)=x+(1-x)x^(3)+(1-x)(1-x^(2))x^(3)+.........+(1-x)(1-x^(2))......*(1-x^(n-1))x^(n);(n>=4) then :

lim_(x rarr0)((1+x)^((1)/(3))-(1-x)^((1)/(3)))/(x)=(2)/(3)

lim_(x rarr0)((1+x)^((1)/(3))-(1-x)^((1)/(3)))/(x)=(2)/(3)

lit_(x rarr0)((1+x)^((1)/(3))-(1-x)^((1)/(3)))/(x)=(2)/(3)

lim_(x rarr0)((1+x)^((1)/(3))-(1-x)^((1)/(3)))/(x)=(2)/(3)

((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x+x^(1/2)))^10 find term independent of x

The term independent of x in the expansion of ((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-x^(1/2)))^(10) is -

If (x^(2) + 1)/(x)= 3(1)/(3) and x gt 1 , find x^(3)- (1)/(x^(3))