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                                    The value of Lim_(xto0) (5x^(2)+[x^(2)+1])^(((1)/(x^(2)+sin^(2)x))) is, [Note : [y] denotes greatest interger less than or equal to y.] | 
                            
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Answer»  `(5)/(2)` where `L=underset(xto0)Lim(1)/(x^(2)+sin^(2)x)(5x^(2)+[x^(2)+1]-1)=underset(xto0)Lim(5x^(2))/(x^(2)+sin^(2)x)=(5)/(2)` `:."Limit"=e^((5)/(2))`.  | 
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