Let `0ltxlt1` , then `sqrt(x-1)^2+((2x+1)^4)^(1/4)-((x-1/2)^3)^(1/3)` is

sqrt(2^x(4^x(0. 125)^(1/ x))^(1/3))=4.(2^(1/3))

If 0ltxlt1 , then tan^(-1)(sqrt(1-x^(2))/(1+x)) is ____

If 0ltxlt1 then sqrt(1+x^(2))[{x cos (cot^(-1)x)+sin(cot^(-1)x}^(2)-1]^(1/2)

If 0ltxlt1 then tan^(-1)(sqrt(1-x^(2))/(1+x)) is equal to

sqrt(2^(x)(4^(x)(0.125)^((1)/(x)))^((1)/(3)))=4.(2^((1)/(3)))

Without expanding, find the value of: (i) (x + 1)^4 - 4(x + 1)^3 (x - 1) + 6(x + 1)^2 (x - 1)^2 - 4(x + 1) (x - 1)^3 + (x -1)^4 (ii) (2x - 1)^4 + 4(2x - 1)^3 (3 - 2x) + 6(2x - 1)^2 (3 - 2x)^2 + 4(2x - 1) (3 - 2x)^3 + (3 - 2x)^4

lim_(x-> -1) (x+1)/(sqrt(x^2 + 3) -2) = (1) -2 (2) 1/2 (3) 2 (4) 0

Degree of the polynomial (x^(2)-sqrt(1-x^(3)))^(4)+(x^(2)+sqrt(1-x^(3)))^(4) is

If (3sqrt4)^(2x+1/2)=1/32 , then x =