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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.]A. `(5)/(2)`B. `e^((5)/(2))`C. `(25)/(2)`D. `e^((25)/(2))` |
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Answer» Correct Answer - A `underset(xto0)Lim(5x^(2)+[x^(2)+1])^(((1)/(x^(2)+sin^(2)x)))=e^(L)` 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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