C. Choose the correct answer below. A. The statement is false because the error in the Trapezoid Rule is proportional to \( \frac{(\Delta x)^{2}}{12} \) B. The statement is true because the error in the Trapezoid Rule is proportional to \( (\Delta x)^{2} \) C. The statement is false because the error in the Trapezoid Rule is proportional to \( (\Delta x)^{4} \). D. The statement is false because the error in the Trapezoid Rule is proportional to \( \Delta x \).

The Trapezoid Rule is a numerical method used for estimating the definite integral of a function. Its error term is actually related to the second derivative of the function being integrated. Specifically, the error is proportional to \( \frac{(\Delta x)^{2}}{2} \times f''(c) \), where \( c \) is some point in the interval of integration. This is based on the fact that the accuracy improves as the interval width \( \Delta x \) decreases. In practical terms, if you're using the Trapezoid Rule to estimate an area under a curve, it’s always good to start with a sufficiently small \( \Delta x \). However, a common mistake is assuming that halving \( \Delta x \) will halve the error; in reality, it squares the accuracy, meaning your results could become significantly better more quickly than expected!