Prove that `root(3)(x^(3)+7)-root(3)(x^(3)+4)` is approximately equal to `(1)/(x^(2))` when `x` is large.

Prove that root(3)(x^(3)+6)-root(3)(x^(3)+3) is approximately equal to 1/x^(2) when x is sufficiently large.

Prove that root(3)(x^3+6)-root(3)(x^3+3) is approximately equal to (1)/(x^2) when x is sufficiently large.

Integrate root (3) (x^(4))

Solve : root(4)(|x-3|^(x+1))=root(3)(|x-3|^(x-2)) .

Find the roots of the equation x+(1)/(x)=3, x ne 0

If ((1-3x)^(1//2)+(1-x)^(5//3))/(sqrt(4-x)) is approximately equal to a+bx for small values of x , then (a,b)=

Let k(x) = ((x^(2)+1))/(root(3)(x^(3)+3x+6) dx and k(-1) = 1/root (3)(2)) then the value of k(-2) is

Solve the equation x^(3)+5x^(2)-16x-14=0 given x+7 is a root

Evaluate lim_(xto1)(root(3)(7+x^3)-sqrt(3+x^2))/(x-1)