Draw the graph and discuss the continuity of `f (x) = [sin x + cos x], x in [0, 2pi),` where [.] represents the greatest integer function.

Explanation

To solve the problem of drawing the graph and discussing the continuity of the function \( f(x) = \lfloor \sin x + \cos x \rfloor \) for \( x \in [0, 2\pi) \), we will follow these steps:

### Step 1: Analyze the Function
We start with the function \( f(x) = \lfloor \sin x + \cos x \rfloor \). To understand this function, we need to analyze the expression \( \sin x + \cos x \).

### Step 2: Find the Maximum and Minimum Values of \( \sin x + \cos x \)
The maximum value of \( \sin x + \cos x \) can be found using the identity:
\[
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