`l i t_(x->0)((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)

Let L= lim_(x->0) (a-(a^3-x^3)^(1//3) - x^3/108)/(x^6); a>0 If L is finite, then L is

Value of ((x-1)^(3)+(2x-1)^(3)-(3x2)^(3))/((x-1)(2x-1)(3x-2)) is equal to (A)-3(B)0(C)1(D)3

Prove that: i) sin^(-1)(3x-4x^(3))=3sin^(-1)x, |x| le 1/2 ii) cos^(-1)(4x^(2)-3x)=3cos^(-1)x,1/2 le x le 1 iii) tan^(-1)""(3x-x^(3))/(1-3x^(2))=3tan^(-1)x, |x| lt 1/sqrt(3) iv) tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)""(3x-x^(3))/(1-3x^(2))

Let l_(1)=int_(0)^(1)(e^(x))/(1+x)dx and l_(2)=int_(0)^(1)(x^(2))/(e^(x^(3))(2-x^(3)))dx. "Then"(l_(1))/(l_(2)) is equal to

Let l_(1)=int_(0)^(1)(e^(x))/(1+x)dx and l_(2)=int_(0)^(1)(x^(2))/(e^(x^(3))(2-x^(3)))dx. "Then"(l_(1))/(l_(2)) is equal to