Recall the function $\arctan(x)$, also denoted as $\tan^{-1}(x)$. Complete the sentence: $$\arctan(20202019) + \arctan(20202021) \quad\underline{\hspace{2cm}}\quad 2\arctan(20202020),$$ because in the relevant region, the graph of $y = \arctan(x)$ $\_\_\_\_$. Fill in the first blank with one of the following: is less than / is equal to / is greater than. Fill in the second blank with a single correct reason consisting of one of the following phrases: is bounded / is continuous / has positive first derivative / has negative first derivative / has positive second derivative / has negative second derivative / has an inflection point.
Recall the function $\arctan(x)$, also denoted as $\tan^{-1}(x)$. Complete the sentence:
$$\arctan(20202019) + \arctan(20202021) \quad\underline{\hspace{2cm}}\quad 2\arctan(20202020),$$
because in the relevant region, the graph of $y = \arctan(x)$ $\_\_\_\_$.
Fill in the first blank with one of the following: is less than / is equal to / is greater than. Fill in the second blank with a single correct reason consisting of one of the following phrases: is bounded / is continuous / has positive first derivative / has negative first derivative / has positive second derivative / has negative second derivative / has an inflection point.