Step 1: Analyzing the Math.ceil() Function:
The Math.ceil(x) (ceiling) function rounds its argument $x$ upward to the nearest larger mathematical integer.
$$\text{Math.ceil}(x) = \lceil x \rceil = \min \{ n \in \mathbb{Z} \mid n \ge x \}$$
Step 2: Comparing with Other Rounding Functions:
To understand this better, let's look at the three primary rounding methods in JavaScript for the value $3.14$:
• {Math.floor(3.14): Rounds downward to the nearest integer $\rightarrow 3$.
• {Math.round(3.14): Rounds to the nearest integer mathematically ($\ge 0.5$ rounds up, $< 0.5$ rounds down) $\rightarrow 3$.
• {Math.ceil(3.14): Rounds upward to the nearest larger integer, regardless of the decimal fraction value $\rightarrow 4$.
Step 3: Conclusion:
Because $3.14$ has a decimal component, rounding up moves it to the next larger integer, which is $4$.