Prove that `underset (x rarr 0)lim (x^2 sin (1/x))/sin x=0`

Find underset(x rarr 0)lim (1-cos x)/x .

Evaluate underset (x rarr 0)Lt (sin 3x+7x)/(3x+sin 7x)

(a)Evaluate underset (x rarr 0)Lt(sin x^0)/x

Evaluate underset (x rarr 0)lim(cosec x-cot x)

Choose the most appropriate answer from those given in the bracket. underset(x rarr 0)lim (sin ax)/(xcosbx) =……….. [0, a, b, not defined].

Evaulate underset (x rarr 0)Lim (cos 2x-1)/(cos x-1) .

Evaluate underset(x rarr 0)Lt (tan x-sin x)/(x^3)

lim_(x rarr 0) (tan x- sin x)/x^3

If x is in radian underset (x rarr 0)Lt (sin x)/x=………….