If \( z=e^{x-y} \cos (x-y) \), determine \( \frac{\partial z}{\partial y} \)

Determine if the integral converges or diverges: \( \int_{0}^{1} \frac{1}{\sqrt{x}} \, dx \)

Find the average value of the function on the given interval. \( f(x)=3 x^{2}-4 ;[0,22] \)

Evaluate the integral \( \int \ln(x) \, dx \) using integration by parts.

\( \int \frac { ( x ^ { m } + x ^ { n } ) ^ { 4 } } { x } = \)

Find the integral. \( \int 9 z \sqrt{3 z^{2}-7} d z \) A. \( \left(3 z^{2}-7\right)^{3 / 2}+C \) B. \( z\left(3 z^{2}-7\right)^{3 / 2}+C \) C. \( \frac{1}{2}\left(3 z^{2}-7\right)^{3 / 2}+C \) D. \( \frac{1}{2} z\left(3 z^{2}-7\right)^{3 / 2}+C \)