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If f(x)=sin^(-1)x then prove that ("lim"...

If `f(x)=sin^(-1)x` then prove that `("lim")_(nvec1/2),f(3x-4x^3)=pi-3("lim")_(nvec1/2),sin^(-1)xdot`

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`sin^(-1) (3x -4x^(3)) = pi - 3 sin^(-1) x " if " (1)/(2) lt x lt 1`
`:. underset(x rarr (1)/(2))("lim") f(3x - 4x^(3)) = underset(x rarr (1)/(2))("lim") (pi - 3 sin^(-1) x)`
`= pi - 3 underset(x rarr (1)/(2))("lim") sin^(-1) x`
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