underset x rarr01(sin4x)/(1-sqrt(1-x))" is "

Evaluate the following limits underset (x rarr 0)Lt (sqrt (1+x)-sqrt(1-x))/x

lim_(x rarr 0) sin(4x)/(1-sqrt(1-x)) equals

Prove that underset (x rarr 0) lim (sin x)/x=1 ,where x is in radian and hence evaluate: underset(x rarr 0)lim (sin 4x)/(sin 2x) .

Evaluate : underset( x rarr0 ) ("lim") ( sqrt( ( 1+sin 3x))-1)/(ln ( 1+ tan 2x))

lim_(x rarr 0) (sin x)/(sqrt(x + 1) - sqrt(1-x)) is :

Evaluate : underset(x rarr a)lim (sin sqrt(x) - sin sqrt(a))/(x-a)

Prove that , underset(x rarr 0)lim (sqrt(1-cos x))/(x) does not exist.

(ii)Find underset (x rarr a)Lt(cos x-sin a)/(sqrt x-sqrt a) .