Solve the problem. The Van der Waals equation provides an approximate model for the behavior of real gases. The equation is

Solve the problem.The radius r and height h of a cylinder are changing with time. At the instant in question, x = 3 cm, h= 5 cm, dx/dt = 0.02 cm/sec and dh/dt = -0.02 cm/sec.  At what rate is the cylinder’s volume changing at that instant?

(Select all that apply.)If

Give an appropriate answer.Express the following in subscript notation. (i)

Find  by using the Chain Rule. Express your final answer fully simplified in terms of t.w = x3y2;      x = t2,      y = t5 Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu. 

Determine whether the given function satisfies the Laplace equation:

Determine whether the given function satisfies the Laplace equation for 3 variables:  

Consider the function: 

Give an appropriate answer.If f(x, y, z) = x2y2 + xyz + y2z2 find fxz(x, y, z).

At what points is the given function continuous?