### Question 1 **True or False:** Evaluate the statement: \[ \frac{d}{dx} \left[ 2 + \frac{1}{x} \right] = -\frac{1}{x^2} \] - **False** (selected) - True ### Explanation: This is a calculus question asking if the derivative of the function \( f(x) = 2 + \frac{1}{x} \) with respect to \( x \) is equal to \( -\frac{1}{x^2} \). To solve this, use the power rule for derivatives. The derivative of \( 2 \) is 0, and the derivative of \( \frac{1}{x} \) which is \( x^{-1} \) is calculated as follows: \[ \frac{d}{dx} \left( x^{-1} \right) = -1 \cdot x^{-2} = -\frac{1}{x^2} \] So, the derivative \(\frac{d}{dx} \left[ 2 + \frac{1}{x} \right]\) is indeed \(-\frac{1}{x^2}\). Therefore, the answer should be **True** instead of False.