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Evaluate (lim)(hvec0)((a+h)^2sin^(-1)(a+...

Evaluate `(lim)_(hvec0)((a+h)^2sin^(-1)(a+h)-a^2sin^(-1)a)/h`

Text Solution

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`underset(hrarr0)lim((a+h)^(2). sin ^(-1)(a+h)-a^(2) sin^(-1) a)/(h).`
`=(d)/(da)(a^(2) sin^(-1) a)`
`=(sin^(-1)a) (d)/(da)(a^(2)) +(a^(2))(d)/(da)(sin^(-1)a)`
`=(a^(2))/(sqrt(1-a^(2)))+2a sin^(-1)a`
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