Limit question

Question

$\lim_{x\rightarrow0}\frac{x^{2}+1}{x(x-1)}=?$

Comments

I don't think you limit conversion part is ok.

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Sir,

1/x is going to infinity still you have taken 1/x and 1/x² as 0.

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yes Ashwin, thanks.

Answer 1

limit 1st rule 1st substitute  x->0   we get  1/0    =  infinity    infact we  get   Left hand limit = +infinity  and Right hand limit = - infinity

infinity ↑    not and indeterminant form

since LHL not equal to RHL  its answer is does not exist  , infinity is not a number  we cannot say answer is infinity