Stanley Campbell

10/15/2024 · Junior High School

For the function below, write the differential. \[ f(x)=x^{1 / 2}+x^{1 / 3} \] \( d y=\left(\frac{1}{2} x^{-\left(\frac{1}{2}\right)}+\frac{1}{3} x^{-\left(\frac{2}{3}\right)} d x\right. \) Calculate \( d y \) for the given values of \( x \) and \( d x \). (Round your answer to four decimal places.) \( \quad x=125 \) and \( d x=-0.5 \) \( d y=0581 \) How accurate is \( d y \) in approximating \( \Delta y \) (i.e., what is their difference) to the nearest thousandth?