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Let f(x)=sin^(-1)((x+3)/(2x+5)),g(x)=sin...

Let `f(x)=sin^(-1)((x+3)/(2x+5)),g(x)=sin^(-1)((ax^(2)+b)/(x+5))`. If `lim_(xto oo) (g(x)-f(x))=(pi)/3` and `lim_(x to 0) (f(x)+g(x))=(pi)/4` then value of `(a^(2)+b^(2))`

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