Answer
Divergent
Work Step by Step
Simplify the improper integral $\int_0^{2{-}} \dfrac{\ dx}{x-2}$
Let us consider that $I=\lim\limits_{z \to 2^{-}} \ln (x-2)$
Integrate the integral by using limits.
$I=\lim\limits_{z \to 2^{-}} [\ln |z-2|-\ln (2)]\\=-\infty$
So, the given integral is divergent.
