Question

Find the limit
x tends to 2
(x^2+4x–1)/(x^2–2x)

Answer 1

$\lim{x\ \rightarrow2}{\frac{x^2+4x-1}{x^2-2\ x}}$

$\lim{x\ \rightarrow2}{\frac{\frac{x^2}{x^2}+\frac{4x}{x^2}-\frac{1}{x^2}}{\frac{x^2}{x^2}-\frac{2x}{x^2}}}$

\frac{1+\frac{4}{2}-\frac{1}{4}}{1-\frac{2}{2}}=\frac{\frac{5}{4}}{0}\

The limit is undefined