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Which of the following limits exists finitely? |
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Answer» `underset(xrarr0^(+))(lim)(x)^(log_(E)x)` So, limits does not exist finitely. (b) `underset(xrarr3)(lim)(x^(2)-9-sqrt(x^(2)-6x+9))/(|x-1|-2)` `=underset(xrarr3)(lim)(x^(2)-9-|x-4|)/(x-3)` Now, `f(3^(+))=underset(xrarr3^(+))(lim)((x^(2)-9)-(x-3))/((x-3))=underset(xrarr3^(+))(lim)((x+3)+1)=5` ALSO, `f(3^(-))=underset(xrarr3^(-))(lim)((x^(2)-9)+(x-3))/((x-3))=underset(xrarr3(-))(lim)((x+3)+1)=7` So, LIMIT does not exist. (c) `underset(xrarr3^(-))(lim)([x])^((1)/(x-1))underset(xrarr1^(+))(lim)^((1)/(x-1))=1` |
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