Limits of tolerance

$\begin{aligned} L & = \lim_{x \to 0} \left(\left \lfloor 200\cdot \frac {\color{#3D99F6}\sin x}x \right \rfloor + \left \lfloor 194\cdot \frac x{\color{#3D99F6}\tan x} \right \rfloor \right) & \small \color{#3D99F6} \text{By Maclaurin series} \\ & = \lim_{x \to 0} \left \lfloor 200\cdot \frac {\color{#3D99F6}x-\frac {x^3}{3!}+\frac {x^5}{5!}-\cdots}x \right \rfloor +\lim_{x \to 0} \left \lfloor 194\cdot \frac x{\color{#3D99F6}x+ \frac 13x^3+\frac 2{15}x^5+\cdots} \right \rfloor \\ & = \lim_{\color{#D61F06}x \to 0^\pm} \left \lfloor 200\cdot \frac {\color{#3D99F6}x-\frac {x^3}{3!}+\frac {x^5}{5!}-\cdots}x \right \rfloor +\lim_{\color{#D61F06}x \to 0^\pm} \left \lfloor 194\cdot \frac x{\color{#3D99F6}x+ \frac 13x^3+\frac 2{15}x^5+\cdots} \right \rfloor & \small \color{#D61F06} \text{For both }\lim_{x \to 0^+} \text{ and }\lim_{x \to 0^-} \\ & = \left \lfloor 200\cdot {\color{#3D99F6}1^-} \right \rfloor +\lim_{\color{#D61F06}x \to 0^\pm} \left \lfloor 194\cdot {\color{#3D99F6}1^-} \right \rfloor \\ & = 199+193 = \boxed{392} \end{aligned}$