Q#1 Verify Divergence Theorem for F =x?i+zj+ yzk, taken over the cube bounded by x= 0, x = 1, y = 0, y = 1, z = 0, z = 1.

Solve this.

Use the e-S definition of infinite limits to prove the statement. lim -00 %3D X - X→5 f(x) 1 is defined for all x # Let N 0 such that f(x) ---Select--- V < ---Select--- v Thus lim = -0, |x - 5| х — 5 |x – 5| X→5- X

In the canonical ensemble, we control the variables T, p, and N, and the fundamental function is the Gibbs free energy (G). But if we control T, p, and μ, then we will have a different fundamental function, Z (This is the case for cells that often regulate their temperature, pressure, and chemical potentials to maintain equilibrium). Which of the below options should the Z function equal? H - TS - μN H + TS + μN H + TS - μN G + μN F - pV - μN -H + TS + μN