The largets value of non negative integer for which `lim_(x->1){(-a x+sin(x-1)+a]1-sqrt(x))/(x+sin(x-1)-1)}^((1-x)/(1-sqrt(x)))=1/4`

The largets value of non negative integer for which lim_(x rarr1)((-ax+sin(x-1)+a]1-sqrt(x))/(x+sin(x-1)-1)}^((1-x)/(1-sqrt(x)))=(1)/(4)

The largest value of non-negative integer a for which underset( x rarr 1 ) ( "lim"){ ( -ax+ sin ( x - 1) + a ) /(x + sin ( x - 1) -1)}^((1-x)/( 1- sqrt( x)) ) = ( 1)/( 4) is

(x.sin^(-1)x^(2))/(sqrt(1-x^(4)))

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

sqrt((1+sin x)/(1-sin x))

lim_(xrarr0) (sin4x)/(1-sqrt(1-x)) , is

lim_(x rarr 1)(1-sqrt(x))/(1 + sqrt(x))

lim_(x rarr1)(sqrt(x^(2)-1)+sqrt(x-1))/(sqrt(x^(2)-1))

lim_(xrarr0) (sin4x)/(1-sqrt(1-x))=?

lim_(xto0)(sin2x)/(1-sqrt(1-x))