Question

Can somebody check if my work is correct

Answer 1

Show that f(x) = \[\frac{ 2x+3 }{ x-2 }\] is continuous on the interval (2,inf)

Answer 2

\[\lim_{x \rightarrow a}f(x)=\lim_{x \rightarrow a}\frac{ 2x+3 }{ x-2 }\]
\[=\frac{ \lim_{x \rightarrow a}2x+3 }{ \lim_{x \rightarrow a}x-2 }\]
\[=\frac{ 2a+3 }{ a-2 }\]
\[=f(a)\]