(ii) `lim_(xto0) ((1+x)^3-(1-x)^3)/x`

Slove lim_(xto0)((1+x)^(1//x)-e)/x

lim_(xto0)((e^(x)-1)/x)^(1//x)

Find lim_(xto0)(cot^(-1)(1/x))/x

Find the following limits: (i)lim_(xto0) (1)/(x)sin^(-1)((2x)/(1+x^(2)))" "(ii)lim_(xto0) (1)/(x)sin^(-1)(3x-4x^(3))

Find the following limits: (i) lim_(xto0) (1-x)^((1)/(x))" "(ii) lim_(xto1) (1+log_(e)x)^((1)/(log_(e)x)) (iii)lim_(xto0) (1+sinx)^((1)/(x))

Evaluate lim_(xto0) ((x+2)^(1//3)-2^(1//3))/(x)

Find the limits of the following: (i)lim_(xto0) (sin3x)/(x)" "(ii)lim_(xto0) (sin7x)/(sin4x)" "(iii)lim_(xto0) (1-cos^(2)x)/(x^(2))

If lim_(xtoa)f(x)=1 and lim_(xtoa)g(x)=oo then lim_(xtoa){f(x)}^(g(x))=e^(lim_(xtoa)(f(x)-1)g(x)) lim_(xto0)((a^(x)+b^(x)+c^(x))/3)^(2/x) is equal to

Evaluate lim_(xto0) ((1+x)^(1//x)-e+(1)/(2)es)/(x^(2)) .

If lim_(xto0) (log (3+x)-log (3-x))/(x)=k , the value of k is