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

lim_(x rarr1)[((4)/(x^(2)-x^(-1))-(1-3x+x^(2))/(1-x^(3)))^(-1)+3(x^(4)-1)/(x^(3)-x^(-1))]

L_(x rarr1)[(x-1)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+x)]

lim_(x rarr1)[(x-1)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+x)]

If x^(2)+3x+1=0 then find x^(3)+(1)/(x^(3)),x^(4)+(1)/(x^(4)),x^(2)-(1)/(x^(2)),x^(2)+(1)/(x^(2))

IF 3 sin^(-1)((2x)/(1+x^(2)))-4cos^(-1)((1-x^(2))/(1+x^(2)))+ 2tan^(-1)((2x)/(1-x^(2)))=(pi)/3 then x=

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

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

If D(x)=det[[(x-1),(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+1)^(3) then the coefficient of x in D(x), is ]]

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))

If x+(1)/(x)=3, calcuate x^(2)+(1)/(x^(2)),x^(3)+(1)/(x^(3)) and x^(4)+(1)/(x^(4))