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

Now that we are half-way through the semester, what challenges are you facing in this course?  How can you overcome them and persevere?    Is there anything else you want to tell me, either about yourself or about the class?

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

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

Find the limit.  Give exact answers only.  

Find the value.Find F(f(t), g(t))    if    F(x, y) = xy2    and    f(t) = t3 sin2t,    g(t) = 4 csc t 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.  Be sure to fully simplify your answer!!! (No fractions, no negative exponents, no radicals, least number of trig functions, etc.)

Find the limit.  Give exact answers only. 

Find the value.Let

The position vector of a particle is r(t). Find the requested vector.The velocity at t = 3 for r(t) = (9t2 + 4t + 7)i – 5t3j + (2 – t2)k

Calculate the arc length of the indicated portion of the curve r(t). r(t) = (8 + 2t3)i + (2t3 – 2)j + (5 – t3)k ; -1 ≤ t ≤ 2