Show : `lim_( x -> 0 ) tan^(-1)x/ sin^(-1)x` = 1

Evaluate : lim_( x -> 0 ) ( x - tan^(-1 ) x ) / ( x - sinx )

If I_(1)=lim_(xto 0)sqrt((tan^(-1)x)/x-(sin^(-1)x)/x) and I_(2)=lim_(xto0)sqrt((sin^(-1)x)/x-(tan^(-1)x)/x) , where |x|lt1 , which of the following statement is true?

lim_(x rarr0)(a^(sin x)-1)/(sin x)

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

lim_ (x rarr0) (sin x-tan x) / (tan ^ (- 1) x-sin ^ (- 1) x) =

lim_(x rarr0)(tan^(-1)x-sin^(-1)x)/(sin^(3)x), is equal to

The value of lim_(|x| rarr oo) cos (tan^(-1) (sin (tan^(-1) x))) is equal to

Show that : Lim_(x rarr0)(e^(x)-sin x-1)/(x)=0

lim_(x to 0)(x)/(tan^(-1)2x) is equal to