" if they exist: "((1+x)^(1/3)-(1-x)^(1/3))/(x)

Evaluate the following limits, if they exist : lim_(x to 1)(x^(3)-x^(2)+1)

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)

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)

Evaluate the following limit if they exist : lim_(x rarr -1) (x^3-3x+1)/(x-1) .

Evaluate the following limit if they exist : lim_(x rarr 1) (x^3-x^2+1) .

int dx/(x(1+root(3)(x))^2) is equal to : (i) 3log(x^(1/3)/(1+x^(1/3))+1/(1+x^(1/3)))+C (ii) 3log(((1+x^(1/3))/x^(1/3))+1/(1+x^(1/3)))+C (iii) 3log(((1+x^(1/3))/x^(1/3))+1/(1+x^(1/3)))+C (iv) none of these

Discuss the existance of Lt_(x to 1)(1+5x^(3))/(1-x^(2))

Let f: RvecRf(x)=x^3-3x^2+3x-2, then f^(-1)(x) is given by 1+(x+1)^(1/3) (2) 1+(x-1)^(1/3) x+1 3-1 (4) x-1 3-1