`2. lim_(x rarr1)(x^2+x+2x-4)/(x^3+3)`

lim_(x rarr0)(2x^2-3x)/x

lim_(x rarr0)(1+2x)^(5/x)

lim_(x rarr0)(1-cos 2x)/(x^(2))

lim_(x rarr0)(sin^2x)/(1-cosx)

3. lim_(x rarr0)(sin x sin^(-1)x)/(x^(2))

lim_(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

lim_(x rarr 2) (x^6-24 x-16)/(x^3+2x-12)

Evaluate: lim_(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

1. lim_(x rarr0)(sin^(-1)x-sin x)/(x^(3))

If f(x) = sin^(-1) x then prove that lim_(x rarr (1^(+))/(2)) f(3x -4x^(3)) = pi - 3 lim_(x rarr (1^(+))/(2)) sin^(-1) x