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

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

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

lim_(x rarr0)(x-sin x)/(tan^(3)x)

lim_(x rarr0)(x-sin x)/(tan^(2)x)

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is

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

lim_(x rarr0)(x-sin x)/(tan^(2)x) .

(i) lim_(x rarr0)(x-sin x)/(tan^(3)x)

lim_(x rarr0)sqrt(x)=

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