Question

May someone do this all full steps of this limit limit of x -> 1+ (x-1)/(sqrt(2x-x^2)-1.

Answer 1

\[\lim_{x \rightarrow 1}\frac{ x -1 }{ \sqrt{2x -x ^{2}}-1 }\]\[=\lim_{x \rightarrow 1}\left( \frac{ x -1 }{ \sqrt{2x -x ^{2}}-1 } \right)\left( \frac{ \sqrt{2x -x ^{2}}+1 }{ \sqrt{2x -x ^{2}}+1 } \right)\]\[=\lim_{x \rightarrow 1}\frac{ (x -1)(\sqrt{2x -x ^{2}}+1) }{ 2x -x ^{2}-1 }\]\[=\lim_{x \rightarrow 1}\frac{ (x -1)(\sqrt{2x -x ^{2}}+1) }{ -(x ^{2}-2x +1) }\]\[=\lim_{x \rightarrow 1}\frac{ (x -1)(\sqrt{2x -x ^{2}}+1) }{ -(x -1)^{2} }\]\[=\lim_{x \rightarrow 1}\frac{ -(\sqrt{2x -x ^{2}}+1) }{ x -1 }\]\[=\frac{ -2 }{ 0 }\]which is undefined. ∴ the limit does not exist.

Answer 2

Did you understand @viniterranova ?

Answer 3

Thanks a lot.