Past exam of the mathematical methods II course of the University of Oxford / 2015 resit / 2 / b

Combine the two singular terms before taking the limit:For $x$ near zero, within the real domain $x>-1$, the Maclaurin series is $\log (1+x)=x-x^2/2+O(x^3)$. HenceThe two individual terms have divergent limits; their leading singularities cancel. Evaluating them separately as an “infinity minus infinity” subtraction would not justify the finite result.