Checking a limit equality [closed]

Let's suppose we have a some special point in the $x$ axis. Let me denote it as $x_{\dagger}$. Let us set two points such that, $x_p = x_{\dagger} + \delta x$ and $x_n = x_{\dagger} - \delta x$,for $\delta x > 0$. Let us also take some random function $f(x)$. From here, can we write

$$\lim_{\delta x \to 0}f(x_p) \equiv \lim_{x \to x_{\dagger}^{+}}f(x_{\dagger})$$

and

$$\lim_{\delta x \to 0}f(x_n) \equiv \lim_{x \to x_{\dagger}^{-}}f(x_{\dagger})$$ ?

Solution 1:

I think you had the right idea. If you write it like $$\lim_{\delta x \to 0}f(x_p) \equiv \lim_{x \to x_{\dagger}^{+}}f(x)$$ it is correct. The other case works in the same way.