Taylor expansion for left&right limit

Question

I must find the left and the right limits of a function. Can I use the Taylor expansion (at $x_0$) in order to evaluate them?

Answer 1

Not necessarily. The Taylor expansion may not exist at $x_0$. For example, using the Heaviside theta function $\Theta(x)$ and $x_0=0$, one obtains $$\lim_{x\rightarrow 0^+}\Theta(x)=1\\\lim_{x\rightarrow 0^-}\Theta(x)=0$$ whereas the Taylor expansion of $\Theta$ at $0$ does not exist.