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Find the following limits: (i)lim(xto0) ...

Find the following limits: `(i)lim_(xto0) (1)/(x)sin^(-1)((2x)/(1+x^(2)))" "(ii)lim_(xto0) (1)/(x)sin^(-1)(3x-4x^(3))`

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(i) We know that `sin^(-1)((2x)/(1+x^(2)))=2tan^(-1)x," for "-1lexle1`
`implies" "underset(xto0)lim(1)/(x)sin^(-1)((2x)/(1+x^(2)))=underset(xto0)lim(2tan^(-1)x)/(x)=2`
(ii) We know that `sin^(-1)(3x-4x^(3))=3sin^(-1)x," for "-1//2lexle1//2`
`implies" "underset(xto0)lim1/xsin^(-1)(3x-4x^(3))=underset(xto0)lim(3sin^(-1)x)/(x)=3`
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