Question

f(x)=(x-1)/(x^(2/3)-1)
find the vertical asymptotes and their limits as a approaches from the left and right for both.

Answer 1

\(\large{\bf a^{\frac{{\color{blue} n}}{{\color{red} m}}} = \sqrt[{\color{red} m}]{a^{\color{blue} n}}\\ \quad \\ \quad \\

f(x)=\cfrac{x-1}{x^{\frac{2}{{\color{red}{ 3}}}}-1}\implies f(x)=\cfrac{x-1}{\sqrt[{\color{red}{ 3}}]{x^2}-1}}\\ \quad \\
\textit{vertical asymptotes are at "x" value when the denominator }=0\\ \quad \\
\large{\textit{vertical asympotes }\bf \sqrt[{\color{red}{ 3}}]{x^2}-1=0}\)

Answer 2

as far as finding the one-sided limits, just plug in a few values from the right and left